I keep hearing about there being a huge advantage afforded by black powder firearms, that is usually phrased in general terms. Occasionally people mention armor penetration, but I'm pretty sure a powerful recurve bow can do that too, and has a much higher firing rate. But they take at least an order of magnitude longer to achieve competency with. Is there any other reason besides that to switch to muskets?
Occasionally people mention armor penetration, but I'm pretty sure a powerful recurve bow can do that too
Not really. If you compare this study of muskets and this study of longbows the superiority of musket penetration becomes quite obvious.
A musket (28g ball at 474m/s muzzle velocity) will penetrate 3~4mm of mild steel at 30m, 2mm at 100m. Keep in mind this is a weapon that only takes as much effort required to pull the trigger to use. Accuracy is one thing maybe, but practically anyone can point this at a target and pull the trigger.
A 140 pound longbow (70g arrow at 50m/s muzzle velocity) will just penetrate 2mm of steel at 10m with a bodkin. 10m, that's barely half the shortest distance archery is shot at today (indoors 18m). And 140 pounds is heavy. Not impossibly heavy, longbows have been found as heavy as 180 pounds, but 140 pounds still represents a challenge for anyone who hasn't been shooting a bow all their life. Bows in the 70~100 pound range was far more common, shooting arrows with half the punch of the 140 pound longbow.
So a musket will penetrate as much steel as an arrow from a very strong archer but at 10x the distance. Yes you mentioned recurves which tend to have ~20% better performance, and the data I've provided are about longbows but that's not significant enough to turn the tide. As far as penetration is concerned, muskets win over bows hands down.
I would recommend you look at this answer from our FAQ as an ideal on why bows were replaced with guns, but you are correct on the concept of compentancy.
There are a number of writers from the 16th century who compared firearms to the English longbow and for what it's worth many of them did disagree with the notion that bows had inherently more range and accuracy than firearms, pointing out that a musket shot with good powder could kill an unarmored man at up to 600 yards, while only a very small number of English bowmen could shoot effectively beyond 200-240 yards. English mercenary Humfrey Barwick claimed that just as the crossbow was more accurate than the bow, so was a musket or arquebus more accurate than that, especially if fired from a rest. He wrote that he could reliably hit a man-sized target at up to 120 yards with a musket (assuming good powder and perfectly round balls of the correct size), and doubted that the best Archer in England could reliably do the same.
Barwick even had an explanation for why he thought the difference in maximum rate of fire wasn't a big deal due to the fact that a firearm could start shooting at much longer ranges and at shorter ranges it could be loaded with more than one bullet at a time.