You've already answered the question. Muskets were cheap to make, and got cheaper. They required little training to operate, particularly as the military drill became widespread. Those are huge advantages.

To contrast with horse archers as you do, that's instructive. Riding a horse in combat is difficult, takes years of practice. Archery is difficult, requires a lot of practice, for both man and horse. Shooting from the saddle is thus _very_ hard, combining two difficult skills-- the people who could do it well were soldiers who'd been training for many years, whether we're speaking of Parthians or Japanese samurai horse archers.

As Napoleon observed "God is on the side of the big battalions" -- and musketry allowed for the conscription of minimally trained levies. Military history is filled with simpler, arguably inferior technologies supplanting ones which required more proficiency and couldn't be trained up in large numbers-- think of Japanese medieval armies switching to massed spear formations, a big step down from the proficient swordsman seeking individual combat for glory of earlier eras, but much more cost effective.

This subject returns regularly, so you might be interested in previous responses. I would the following threads in particular:

Response by by u/hborrgg in this and this thread concerning the proposed use of bows in the colonial times and in American Revolutionary War.

This response by u/wotan_weevil about the use of bows in Europe from 16th century onwards.

This response by u/Valkine describing the transition from neurobalistic weapons to gunpowder ones

This thread comparing various traits of both kinds of weapon.

This thread further comparing the two kinds of weapons and general attitude to both.

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As the last part of your question seems to be not covered by the discussions quoted above, let me address it here. The effectiveness of the formations or particular weapon is far from absolute and usually depends heavily on the milieu it is utilized it. Ottomans, Poles and, to lesser extent, also Russians were quite commonly using horse archers (quite often they were simply Tatar mercenaries, most numerous in the Ottoman army) because the fields and steppes spanning from borders of modern Poland to Caucasus facilitated the usage of highly mobile units and chevauchée tactics while at the same time, the nomadic Nogai Tatars from the Budjak and Akerman region and, to lesser extent, also Crimean Tartars provided a lot of recruits trained in both horse riding and archery from the early age. Their effectiveness in open combat was not big, but when supported by other troops, most notably heavy Ottoman cavalry, infantry and artillery, their were very adept at harassing the enemy and limiting their mobility. Furthermore, Poles, Lithuanians and Cossacks living the the southeastern area of the country were also adept at archery largely for the same reasons (they had long traditions and mobile tactics were useful in the region) but this did not translate to general tactics and equipment of the Polish-Lithuanian forces facing different enemies (Swedes, Russians, Danes, Saxons etc.) in different geographical regions. As already mentioned in the discussions quoted above, quality of command discipline and cohesion were paramount to overall effectiveness and thus adoption of new tactics in place of ones that were learned by commanders, officers and soldiers alike was not considered a viable improvement. It is one of the major reasons why the archery, once abandoned, never made it back into western strategy despite the fact that bows themselves were still quite effective weapons on their own.

Tartars utilized tactics suited for the terrain and the character of their campaigns, but Polish and Cossack forces quickly adopted effective countertactics, based on inversion of typical western organization, with cavalry in the middle, protected from the flanks (and sometimes also from the front) by wagons and infantry, although Cossacks preferred more stationary variants of 'Wagenburg', especially when their forces were composed primarily of foot soldiers. Even though that infantry, especially highly praised German mercenary musketeers used protective equipment sparsely, the higher range and power of the firearms was giving Poles an edge, while wagons made it hard for Tartars to attack musketeers in close combat. The downside to this tactics was high level of complication, making the interaction between units and effectiveness of command crucial. Problems with communication and mistakes made by leaders of particular units are considered to be the major reasons for the Polish defeat in the battle of Cecora on 19th September 1620, although despite numerical advantage of almost 5 to 1, Ottoman-Tatar forces (of which at least half was composed of Tatar light cavalry) suffered losses twice as high as casualties on Polish-Lithuanian side. Polish-Lithuanian victories over Ottoman forces, such as at Battle of Khotyn in 1621, Sasowy Rog in 1633, Komarno in 1672 and Khotyn again in 1673 show that the Tatar horse archers were definitely not a factor able to decide the outcome of the battles.

You have two separate ‘worlds’ you’re combing. The Asian world (including the Middle East) and the western world (Europe).

Horse archers were extremely effective and devastated Europe on several occasions (the most famous being the mongols). But that’s a lifetime of riding, hunting, and fighting on horseback to fight well that way. They will actually fully adopt gunpowder weapons later than Europe (cannons and ‘firelances’ excluded). The European knights took as much time to become potent on the battlefield and were a lot less effective after the adoption of these weapons. Imagine infantry and cavalry armed with swords charging a line of muskets.

They also didn’t just have units solely armed with muskets. Early on they were a combination of pikeman and muskets. Look at the Swedish king Gustavus II Adolphus, his main military renovation is adding more muskets to the muskets and pike ratio.

The battles you’re talking about do have exceptionally high casualties for the type of warfare that was occurring. It was like a gentleman’s sport, we’ll go out and fight win some and then next year we might lose some. Not the total war of Nation states that occur during and after Napoleon. More men died in the actual battles after the advent, and use, of muskets rather than in route like previous eras of warfare.

The training time is hugely important to the later use gunpowder weapons mainly during the Napoleonic wars. This is because up until that point the idea arming the common people scared the crap out of the generals and governments. Napoleon started arming every able bodied man of France to fight and this ‘Commonwealth army’ forced other nations to do the same. Napoleon has a famous quote, “you cannot defeat me I spend 30,000 lives a month.”

It’s not until this point that these huge casualties are seen on the battlefield, at least in Europe. You see large amounts during the mongol invasion and their conquests but they were probably inflated. They were also an almost exclusively mounted force, excellent killing machines during a route, and they were pretty brutal and didn’t really take prisoners.

Sorry for all this but there’s not really a simple answer. However, part of why I think it doesn’t make sense to you is because the huge contrast in how wars were fought, mainly the mindset of the people declaring and waging them in Europe, isn’t talked about that much.

Okay there's a lot to unpack here.

So muskets get a bad rap, and it's mostly due to our modern understanding of firearms getting in the way of a realistic assesment of early gunpowder weapons. Muskets are seen as basically really really bad rifles, which is a a point of reference that somebody from the 16th century wouldn't have, you know how they'd look at it? as a stronger crossbow, which makes sense since they had much in common, from being fitted in a wooden stock, could to be 'cocked' and could be fired from a prone position, and indeed oftentimes both weapons were grouped together for that reason. So it makes sense for muskets to exist in a sort of continuum of the ranged weaponry availible in the day from the weaker, but faster bows, all the way to the slower, but much stronger 16th century muskets (not to be confused with 18th century muskets, which were lighter, and also more innacurate but i'll tackle that in a bit). I don't need to crushingly demonstrate the superiority of the musket over the bow, because there was none, but for the time period in question it had a niche of being better at penetrating armor with far less effort, which was a particularly great use for the european armies of the time that had a liking for heavily armored cavalry. In continental Europe crossbows were the norm for light infantry, so the switch to firearms was more natural, but in England, with its centuries old tradition of archery, the change was more gradual, and both weapons would be used in conjunction for most of the 16th century.

Better yet, you could see it as a portable cannon, which is tactically much more flexible and versatile while still delivering a deadly shot. That last one isn't even a stretch, muskets were actually used very much like cannons in the battlefield, and that leads me to the most important reason as to why muskets were so succesful: the tactical defensive.

Yes, funnily enough in the midst of the discussions of accuracy and rate of fire and whatnot, what is often missing is the way in which muskets were actually used in the battlefield, and looking at it it's clear that the weaknesses were minimized and the strenghts maximized. First of all they we have to talk about sieges, in this time sieges were the norm over battles, by a long shot, and behind safe, unmoving walls the musket can reload and shoot with much less hassle than in the battlefield, and the more fortresses you have to man, the more muskets you'll need. It makes much sense then, that the battlefield tactics of the day sought to emulate a sort of siege in which one's army has a privileged, easily defensible position. This is of course not an tactical innovation, this has been known since time inmemorial, but any army that charged against an entrenched, fortified enemy armed with muskets is bound to suffer casualties. Battles of the Italian campaings such as Cerignola and Ravenna were very much like that. The tercio formation is in itself a defensive formation for which the tactics of the day didn't have much of a response, pikes on all sides with ranged support from muskets, it represented a tactical impasse that armies then sought to emulate and innovate upon. This however made battles very costly and dangerous, and thus avoided as much as possible.

Interestingly, the above development occured quasi independently in another part of the world, the middle east and India, The Ottoman empire developed a masterful synthesis of the many military influences they came across, their horse cavalry tradition of the steppes, the musket infantry that was slowly gaininng prominence, and the hussite wagon fort tactics they fought against in the balkans. The Ottomans would place their wagons in formation with cannons and infantry behind, and the cavalry at the wings, the cavalry would then charge and try to lure the enemy by feigning retreat, only to pin them down with massed fire, and then in turn they would charge and crush the shattered army. It worked to great success against the safavids at Chaldiran (1514) and the hungarians at Mohacs (1526). This tactics would later be used by the central asian conqueror Babur in the battles of Panipat and Khanua, which would cement his power over the region and establish the Mughal dynasty in India (The safavids would also acquire firearms but their use is less well documented). Again this is in general terms the application of a defensive strategy using firearms, just better fit for the conditions of central asian warfare, dominated by open terrain and agile horse cavalry. Indeed battles would become rare in this region too, the might of firearms uncontested. The horse archer tradition would very much remain alive in this part of the world though, their tactical effectiveness was unmistakeable, once again, they perfectly existed side by side with musket infantry, better suited for the heavily fortified balkan front for example.

Battles were still a thing though, and again here our modern conceptions of firearms deceive us, since we see soldiers in rigid lines shooting innacurate, slow volleys before engaging in hand to hand combat as a sort of proof of the ineffectiveness of muskets. The thing is that again, we have to understand muskets and musket warfare as far closer to medieval than to modern warfare, and hand to hand combat never stopped being an expected feature of war, as it was in the days of the bow, but any battle where bows were present and the battle was decided by hand to hand combat somehow doesn't seem like a failure of bows... Musketeers were light infantry like the archers of yore, and in the tactical system of the day it was complementary to the pikemen who were the heavy infantry, so the casualties of Breintenfeld aren't out of place at all, they brought the pikes for a reason!

Musket warfare does take a very particular turn in Europe around the 18th century, with the introduction of the bayonet and standardization of the musket as the sole infantry weapon, and is where we get our modern conception of muskets from, slow, innacurate, short ranged, soon to be superseded by better models. But understanding the history of military tactics up to that point makes the picture clearer, the line formations maximized the firepower that the unit could muster in contrast to the much cumbersome tercio squares, volley fire condensing it all into a single punch. The muskets were way lighter by this point to be far more flexible, if less powerful, and the tactics emphasized rate of fire over accuracy by reducing the ball size to better fit the barrel after several rounds. Most importantly, everyone had a musket, plus a bayonet, which made them basically heavy infantry with ranged fire capability, a tremendous tactical asset. Muskets had evolved to fit the necessities of the European battlefield. They kind of "rediscovered" longer ranged muskets in the form of light infantry units equipped with rifles, which were also integral part of their tactics towards the end of the period.

The thing that confuses people when it comes to the musket is ultimately the untapped potential that we nowadays know it has, it was a rather innefficient application of a method for generating kinetic energy which is, in principle, far more effective than that of a bow, releasing tension created by pullin a string, which is tied to and ultimately limited by human strength, compared to the chemical energy released through a combustion reaction, which is not limited by human strength but by other technical concerns, It is thus quite literally replacing manual labor with a machine you just need to learn to operate, or as said more colloquially, "it requires less training", although i think that's slightly misleading, because musketeers could be and often were professional and highly trained soldiers who understood the intricacies of using and maintaining their weapons, and on the flipside bowmen could be and often were poor soldiers who could not afford better equipment. But in the end whatever you can achieve with a bow that you can also achieve with a musket takes lots of training with the former. One discussion is whether or not the english longbowmen could penetrate the heavy armor of the day, another one is whether you'd prefer to train to be able to do that or just use a musket.

Based on the above, the issue of scalability is one that i also want to put forward but with some caveats, because there's a marked difference between the potential and the actual exploiting of it. Looking at the Napoleaonic wars you see the biggest armies that Europe had ever raised up to that point, with the battle of Leipzig, the largest of the wars, having up to 600000 people. The reasons as to why and how the European nations had managed to field such numbers of troops are very difficult to assert and deserves a post on its own, but the very curious thing is that nearly every single infantry soldier in that number had a musket. Now this doesn't mean that muskets equal bigger armies, nor is this number unprecedented on a bigger scale considering the numbers that the Qing and Mughal empires could muster without having their armies wholly comprised of musketeers, what i'm pointing out is that this is the intrinsically superior nature of the musket exploited to its maximum potential, just to give most impactful example of how important the advantage of being easier of use over the bow is.

I agree with amp1212, and would suggest you re-examine your assumptions. about the efficacy of early muskets. Some of the development may have started on a theoretical level ( like Charles V's early investment in improving the technology) but the actual adoption was based on what happened in battle. Throughout the Italian Wars and other conflicts in Europe in the earlier 16th c., armies were equipped with guns, bows, canon etc in varying degrees, and those weapons that resulted in victories were increasingly favored, those that did not were increasingly discarded. After the Battle of Pavia, it was obvious that no one could field an effective army without ranks of muskets.