This has always puzzled me, and probably many other people too. If arrows aren't killing people in armour, then what is? And if arrows are that useless against armoured opponents, then why are the English using the longbow up until the mid 17th century, by which time the musket had become the weapon of choice across Europe, England included, and armour had developed to such a degree as to have been, under the right conditions, bullet-proof? My understanding was that firearms and crossbows were easier to train men to use while the longbow could require a lifetime to master - so again, why did they enjoy such a long period of use?
I can understand their modern-day prestige being put down to romantic tales of Robin Hood and the ability they supposedly granted the common man - that of levelling the playing field with the evil, conniving overlord - but that doesn't explain the fact that their practical use spanned such a large period of time and was so widespread, at least among the English, during that time.
From what I remember reading of the battle of Falkirk, the Welsh archers found their arrows were largely useless against the padded jackets of the Scottish pikemen/spearmen (arranged in schiltron) at a certain distance, which they had to keep for fear of the Scottish knights and archers. But once the Scottish knights and most of the archers had been driven off by the English knights, the Welshmen were able to close to a much shorter distance and at that point apparently found their arrows penetrating quite easily, which allowed them to thin out the Scottish ranks enough for the English knights to move back in and finish the job. It should be stressed that from what I remember, this was a very short distance indeed.
I also recently had a flick through an Osprey book on the subject of the longbow, which mentioned tests run by the English Warbow Society using longbows crafted to the specifications we have on medieval longbows. The EWS don't usually partake in the use of medieval bows and are quick to distance themselves from that misconception, but on this occasion they apparently did give them a try and found that a bodkin arrow fired from a longbow penetrated absolutely anything put in front of it; mail, plate, padding, leather and the combination of all of these a medieval warrior would've worn. The findings they reported were that absolutely nothing was immune to a bodkin fired directly from a longbow beneath a certain range. That last part is important, obviously, but battles such as Falkirk clearly provided archers with the conditions necessary to achieve penetration.
Please don't think I'm actively contradicting anything you've said or trying to start anything other than a discussion; those sources you've cited are pretty unambiguous. I'm questioning rather than arguing, and as you seem to know so much about it I'd like to see what your take is on these things.
Mods, if this is the wrong place for this discussion, just say the word and I'll see about removing this post.