I was very curious about this, we went from a period of chain mail and gambesons to cloth coats. Is the answer as simple as musket balls were strong enough to pierce most of these materials? Were the resources required to craft things like this better used for cannons or more guns? Was it so the army could move faster?
I know that there were regiments of cavalry that wore chest armor and helmets, so why wasn't it more common among infantry?
There's a lot of reasons behind it. More can always be said on the matter, so if anyone would like to put their own oar in, please go right ahead! In the meantime, OP, as I love plate armour (and plate armour loves you!), here are some previous threads for your reading. Since this is a plate armour discussion, we of course turn to u/WARitter, who has answers in the following threads:
To accompany those, u/hborrgg examines specifically why armour started falling out of use in line with gunpowder. Also, it's two centuries down the line, but u/AncientHistory looking at Napoleonic-era cuirassier armour is worth a mention.
You're indeed missing a step between chain mail and gambesons to cloth coats, and it is munition grade armor!
During the 16th and 17th centuries, Musketeers wore little to no armor, usually wearing only a helmet if at all, because they had to be swift in combat to assume tactically advantageous positions, and also they were carrying guns that could be very heavy. But that's usual of light infantry throughout the ages, the ones wearing armor were the heavy infantry, the pikemen, as well as the heavy cavalry, the cuirassiers.
Pikemen were the counterpart to the handgunners, the former providing defense in close combat against cavalry and infantry charges and the latter providing firepower support. Since they engaged in close combat they were heavily armored, with back and breastplates, helmets, tassets, pauldrons and gorgets. To prevent rust, the exterior the of armour could be blackened by applying a mixture of linseed oil and soot; after heating, this left a permanent black layer. Due to cost considerations however some pikemen would actually go to battle with little or no armour, the armoured ones being placed in front of the infantry formation. This was munition grade armour that was of relatively low quality but also cheaper so that it could be mass produced, and it was effective for defending against arquebus shots at long range as well as opposing pikes. Cuirassiers, the heavy cavalry of the day, wore a similar set of armour but of higher quality, called three quarters armour since it dropped leg and lower back armour compared to traditional full plate because it had become too heavy. It was also often bulletproof, which meant that the armour was literally shot with a pistol and the dent would be "proof" that it was of quality. While a musket shot could penetrate it was still useful against long range arquebus shots and pistols as just alluded, as well as blunt weapons such as swords and pikes.
So armor was still in use in the early 17th century and was very good at its job. I wrote more about the effectiveness, logistics and eventual demise of amour in another answer here (with a small bonus of helmet history :p)