Sorry for the slow response. As u/Itsalrightwithme mentioned the chief concern is that you must fight with the army you have, not the army you want, but there are some other reasons that ranged troops generally continued to be considered a secondary importance compared to pikemen and shock cavalry throughout most of the Italian wars. Even the Stradioti, though they sometimes used bows, tended to be better known for their skill with their light lances and ferocity, which made them more willing to get mixed in with the enemy than mounted crossbowmen, mounted arquebusiers, and other light cavalry.

The sudden rise of firearms in the 16th century is was pretty dramatic, but it didn't happen overnight. It involved a lot of experimentation, some of which worked and some of which didn't, as improving technology and tactics slowly made armies with larger proportions of firearms more feasible. Keep in mind that during the Burgundian Wars, Charles the Bold had in his army fairly sizable numbers of cavalry, crossbowmen, and handgunners but still they were brushed aside by the Swiss pikemen. In The Art of War in Italy Taylor notes that when the Swiss marched on Milan in 1511 one in four of them was an arquebusier, an unusually high number at the time. Once the move was aborted, subsequent campaigns saw the number of arquebusiers go back down once again.

First, throughout this period gun technology is generally improving as individuals come up with new designs, new methods of loading, new methods of making powder, etc. At the end of the 15th century especially firearms were really far from uniform, arquebuses came in a wide variety of sizes and calibers, some were designed to be shot from the shoulder, some were designed to be rested against the breast, some had only a short, curved stock which was rested against the cheek. Many weapons still just used a simple, s-shaped lever as a lock, and a number were still essentially just old fashioned handgonnes ignited by hand. Arquebusiers might also still be mixed in with archers or crossbowmen, or even small artillery and swivel guns mounted on carts.

Second, while arquebusiers both on foot and mounted were quickly found to be extremely useful for skirmishing, harassing, and similar actions, figuring how to use them effectively in pitched battles was more difficult. In the late 16th century, Huguenot captain Fracois de la Noue commented on this based on the French Wars of Religion where the Protestant infantry had come to the field well equipped with firearms, but suffered due to a lack of armored pikemen: "It is as if a man should say, that because in the field one harquebuzier may kill a pike man armed with his corcelet, it followeth that in pitcht fieldes the harquebuziers should ouerthrow the battailes of pikes: which neuerthelesse falleth out cōtrarie, for it is certaine that for the most part those battailes [large pike squares] do giue the victorie."

In large battle which involve tens of thousands on each side all of the smoke, noise, fear, and general chaos often meant that even good marksmen struggled to hit anything that wasn't right in front of them. Furthermore, while small numbers of light troops might be able to keep their distance and keep shooting against a slower enemy, the same isn't necessarily true of a dense formation, as the front ranks step back into the men behind them before the rear ranks realize what's going on and a feigned retreat quickly turns into a real one. All this makes finding where to place lots of arquebusiers especially difficult since they can't shoot over the heads of the men in front of them, they need a lot of time to reload, and they are most effective only at a fairly short range. The end result is that for much of the Italian wars, arquebusiers served as essentially the equivalent of the ancient roman velites; a loose cloud of skirmishers which went ahead to harass the enemy and screen the advance of the pike squares, but they generally couldn't be expected to defeat the enemy on their own unless defending a wall, ditch, or other obstacle which could prevent the enemy from actually closing. Adding more arquebusiers didn't really start to help much until the effectiveness and standardization of the weapons began to improve, and various countermarch drills were invented which allowed deep sleeves of shot to fire while staying close to a protective pike square.

With light cavalry during the Italian wars the case was similar. They were incredibly effective at scouting, skirmishing, harassing, raiding, foraging, and seizing defensive positions or setting up ambushes, far more so than the increasingly over-armored gendarmes. But in pitched battles, a large number of horse is even more difficult to turn around on a dime than footsoldiers and european cavalry don't seem to have mastered large scale hit-and-run tactics the same way the mongols did. It was the Battle of Seminara which would largely set the tone for the early part of the Italian wars. Swiss pikemen rolled over the lighter Spanish infantry, and the French Gendarmes easily drove back the javelin-armed Spanish "Jinetes". After the defeat, the Spanish switched to delaying tactics, using their arquebusers and light cavalry to harass the enemy with guerilla warfare while their infantry was reformed to include more pikemen. During the second half of the 16th century lighter forms of cavalry began to hold their their own against heavy lancers due to the use of wheellock pistols, but tellingly this relied on learning to use them as essentially shock weapons rather than at range. According to Sir Roger Williams, he had often seen squadrons of reiters stop and attempt to fire off their pistols from more than 120 yards away, yet still fail to finish turning around before heavy lancers crashed into them. However, if the reiters were "perfect" and charged straight into the lancers without firing at all then they could gain the upper hand as the pistol was more deadly in close quarters than a lance, sword, or mace.

/u/Jan-Pawel-II

This is a matter of the old maxim, namely you fight with the army you have, not the army you wish you could have. This is the most accepted explanation as to why the French were late adopters of pike-and-shot infantry. Even as the 1500s had started, France lacked the firearms industry that her rivals had, in Burgundy, northern Italy, southern Germany, and even in Spain.

Further, the landed aristocrats of France still dominated the political landscape at this time, unlike the city-states of Italy and the ongoing fight between Holy Roman Emperors, his nobles, and the Swiss. Simply put, infantry-centric armies was a way for kings to use money to raise armies instead of having to rely on the older levy system, and the condition in the region around both sides of the Alps had the perfect requirements to enable standing infantry bands for hire.

To quote Mallett and Shaw's Italian Wars:

There is no doubt that the Spanish, and later the Spanish–imperial armies, had an advantage over the French in terms of the quality and achievements of their infantry. It was often remarked that in most parts of France there was no tradition of infantry service and that the social gap between the landed nobility and the peasant classes inhibited the arming of a peasant infantry. Attempts were made during the wars to reorganize the French infantry into permanent regiments officered by nobles, and the legions of 1534 were the final stage of this.

Want to know more? Read through my profile page, I have written quite a bit about the Swiss, Landsknechts, et al.

Thabks for the answers /u/Itsalrightwithme and /u/hborrgg! I will try to find a couple of books about the military developments during the wars.