As said, the longbow was used in mainly in massed volleys, but that doesn't mean the bowmen couldn't aim accurately in other situations. Doesn't mean they could either - I don't know a huge amount about the subject. I suspect however, given how long they spent using the weapons and that most of the soldiers would be professionals, most of the best archers were fairly accurate. As for rate of fire - just got my copy of Barker's
Agincourt open and she gives the numbers as 10 arrows per minute as an absolute minimum demanded, 15 as what a good archer could do, and 20 as the absolute high point.
And since its open, in terms of Toby's thing about payment -
"The wages for the campaign were to be paid quarterly in advance" - so a lot of gold, but not all the gold at once
Re Social Origins of the Medieval Soldier:
"The prospect of earning 6d a day was also attractive to those of higher social rank. Many of Henry V’s archers were yeomen, farmers and minor landholders with incomes in the region of £5 a year, who could afford to equip themselves with a horse and basic armour; some were even younger brothers or sons of gentry whose family purse was not deep enough to provide the king’s host with more than one man-at-arms. For them, military service in France offered the prospect of advancement, and a number of men who were initially recruited as archers would later be found serving as men-at-arms."
Note especially the part about the horse. The vast majority of archers in the Agincourt campaign were mounted when not fighting, which meant they needed to be able to afford a horse (even if they only cost £1 by the values of the time), and needed to be able ride the thing. In both cases, that means money and leisure time - something beyond the resources of the average peasant (although having googled working hours of a medieval peasant they may have had more spare time than I thought).
We also know that some of the archers were probably everyday members of noble households ("From their names, which sometimes occur elsewhere in the accounts in a professional capacity, one can guess that many of this last group were members of the earl’s household: William Coke (the cook), Nicholas Armourer, William Sadelyler, John Foteman, John Fysshelake. One archer is even specifically referred to as a tentmaker.")
Now this is one specific bit of a very large period and I'm not saying that there were no peasants or escaped serfs or what not in Henry's army. But in this case at least, this is what at least one historian says. The whys of this are speculation, but that it happened this way isn't.
And while this is but one example, and that at the tail end of the period, I think it is one of the better ones considering Toby's talking about mercenaries (and I'm not sure mercenary captains would buy their archers bows). We're not talking about fyrds or levies or anything like that - we're talking a small class of pro soldiers.
And in terms of the broader picture - the link between resilient predominantly urban communities and good infantry in this period is a fairly common one. Vebruggen makes it, I think Contamine makes it,
this paper from De Re Militari makes it. Sure, they were a fair few examples of levied infantry, but they were very rarely good. And there's a few examples of good infantry that don't fit this model, but the link is generally sound. And by and large, most commanders didn't use levies when they could. I think
this one from DRM gives a good rundown of why it was never really the norm even early on (and also shows quite clearly the early existence of mercenaries - the Varangian Guard got about 135 grams of gold a month).
Also, I guess that a lot of warriors did not really have too much armour to protect against weapons from directly above - sure helmets, but generally they tried to protect face-to-face with shields and body armour on the horizontal.
They'd wear helmets alright, but the big thing is that you'd want your visor down if arrows were raining and that restricted vision.