He's sort of omiting the part of history where the non skilled farmers who got pressed into the military just beat each other to death with sticks and swords whilst archers shot arrows into the mix.

This is not very good history. Firearms didn’t replace bows and crossbows, nor did crossbows ever fully replace bows. Almost all premodern and early modern Western armies predominantly used melee weapons; eventually, they standardized on the pike. Most Western armies first used firearms in pike-and-shot formations that combined pikemen and arquebusiers. Over time, especially as the arquebus gave way to the flintlock musket, the relative proportions of pikes to firearms shifted towards firearms more and more. The invention of bayonets, which allowed the musket to be used similarly to a pike in close combat, led to the end of pikes.

The musket, and especially the arquebus, was not the lethal and precise kind of firearm we have today. There is a reason the Patriots at Bunker Hill held their fire until they could see the whites of the redcoats’ eyes: if you lost your nerve and shot any sooner than that, you were unlikely to make a lethal hit. The reason musket battles took the form of formations of line infantry exchanging volleys of gunfire is because that was the best way to use the musket, not because Western armies and the men who organized them were stupid.

Which also ties into the training question. Most training at the time focused on close-order formation drills, not on individual prowess. This was true for Napoleonic infantry just as it had been true for pikemen, Roman legions, and Greek phalanxes. Victory depended on line infantry working as a cohesive, disciplined unit that wouldn’t break or shatter easily.

Okay, so what about archers? In the Western context, archers were part of what we today would call “combined arms” to supplement line melee infantry. The idea that “it took many years of practice to build an archer skillful and strong enough to be of use in warfare” is partially true. It was especially true of the English longbow, but that was an outlier in many ways in being an unusually long and heavy bow which could pierce armor. The English longbow requires years of training mostly because of the extreme draw weight, which was atypical among Western bows. It was kind of true for steppe horse archers, except it was less training and more of a way of life for them.

As for “expanding the number of people in a given population that could become soldiers”, training was never a meaningful bottleneck for that in the pre-firearms era. Training time was important for professional soldiers, but the bulk of medieval armies were poorly trained peasants armed with melee weapons, and the bottleneck on calling them up had more to do with the need for farm labor.

But the armies were small and professional until the XIXth century

Written by someone who doesn't know guns and doesn't know bows. I think I got about halfway through. It's just weird. They say the arrow is pressed against the string with the thumb ring on a thumb draw (not how it works) and then there's a picture that clearly shows that's not how it works.