Its a combination of several factors, but it basically boils down to logistics and supply.
Everything you just said was spot-on. The note about skeletal changes in longbow archers we have actual historical evidence for - the English warship Mary Rose sank in the Solent in 1545 and was well-preserved in the bottom mud. When she was raised in 1982 she provided an incredible wealth of archaeological finds, and one of them was the skeletal deformations of many of the crewmen that you mentioned; mirroring a lifetime of practice with heavy-draw bows.
The only thing I can add is that crossbows had similar problems - crossbows were very accurate and very powerful, and additionally didn't require that built-up strength to use, nor the experience to get the most out of the accuracy. Unfortunately the mechanisms that made that possible (especially for the heavier crossbows that used winches requiring gears/sprockets) were expensive to produce, and quarrels have most of the logistical/cost issues innate to arrows. (Note that melting and casting lead is trivial compared to making arrows - you have to balance the shaft, glue on the fletching just-so so it imparts a spin, etc. It's not difficult, but it's much harder to scale up to make lots and lots of ammo. Arwyn's logistical comparison via cartload is
very informative vis a vis why early firearms quickly found favor with many armies even well before technological advancement had pushed the power and accuracy of the nascent technology past the peak of the preceding mature technology.
So, I was pondering afterwards that if the longbow was more accurate, with a higher rate of fire, why (strange as it might seem) was the British Army not using longbows at the Battle of Waterloo. I can think of only three reason, but it would be interesting to hear alternative opinions
Training: I suspect that training someone to shoot accurately with a longbow is a lot harder than training them with a musket
Logistics: You can transport a lot more bullets than arrows given the same transport capacity.
Damage: Not completely convinced on one this one. Arrows have a 'muzzle velocity' of about 120 mph (I asked) whereas the Brown Bess is a 0.75" calibre firing a 1oz ball with a much higher muzzle velocity. Conversely, the war arrows are about three ounces (I asked that too) so the kinetic energy on impact is not going to be too far out.
Anyway, in conclusion, I though it might be interesting if logistics was partly the reason that the British Army didn't use longbows at Waterloo 
About a decade ago I was trying hard to develop my marksmanship skills in my spare time, (as we are wont to do here in Yankeeland) and was frustrated about hitting a seeming wall in my skill, past which I couldn't advance. A more knowledgeable friend gave me a wink and suggested I try a better, more expensive brand of ammunition. To my surprise, my "groupings" (average miss distance from the bulls-eye) improved considerably. Before then I had been suffering (as many shooters do) from a blind faith in the quality of modern manufacturing technology; I'd had no idea that even modern weaponry can have as much mechanical deviation, from round to round, as it actually did. This had hindered my progress as I couldn't tell how much deviation was the firearm's fault, and how much was mine. The angular deviation of a projectile from the intended point of aim is measured in minutes-of-angle; 1/60th of a degree, which equals 1 inch of deviation at 100 yards. (Naturally,
some prefer to use milliradians instead. ) It's a way of formally measuring the average deviation of the projectiles from your weapon.
Once I grasped this, I remembered a statistic I'd read many, many years ago - that the English longbow could put an arrow clean through the arrow-loop of a besieged castle, but it would require
six shots to do so, on average. Being young at the time I hadn't grasped the significance - longbow archers in the Medieval era were true marksmen who were perfectly aware that they could "out-shoot their weapon" and even thought of accuracy in terms of averages just as modern marksmen do. Thus, they'd be familiar with the concept of "minute-of-Deer" accuracy espoused by some American recreational hunters - i.e. there's a non-insignificant cost investment required to acquire or modify to the "sub-MOA" standard, and for many applications it is in excess of requirements. Massed volley fire against enemy soldiers marching in ranks is certainly another example.
But of course it's not always so simple - as the arrow loop example shows, sieges are definitely one place where the more accurate weapon will pay dividends. See also the American Revolution, where the fabled "American longrifle" made good account of itself as a sniper's weapon against British officers, but who's excessive length and slow-loading (due to the rifling gripping the projectile as one tried to ram it home) simply made it inferior to muskets in mass combat, which reloaded faster and had only an area target to contend with. Ranged combat in Antiquity was usually massed shooters raining projectiles on men marching in ranks as well, and had the benefit of being hilariously cheap - rocks could be used for ammo, the sling was but a cord, and you can teach a man to hurl a rock in the general direction of the enemy, and what angle corresponds to what rough range, in an afternoon. And yet the slingers of the Balearic islands were fabled for their skill and much sought after as mercenaries; it was reputed that their children weren't allowed their supper until they could strike the bread loaf with their sling. In other words, they were renowned for their
accuracy, which is of especial note as a sling is very easy to learn to use, but
very hard to master, to gain real accuracy with against a single point target. Clearly, accuracy was of some concern to armies even in Antiquity.
So while the brutal realities of economies-of-scale and logistics will always have their say, the finer points of marksmanship have mattered as well, and our forebears were every bit as knowledgeable about them as we are. Longbows lingered on for a good while even after gunpowder assumed a primary role in war and it's not hard to see why.
