You didn't have just one peasant facing of against one knight, you had dozens of them firing with proper defences. And it didn't take a "pro", that's the whole point of crossbows contra regular bows - they were damn fast to learn to use in comparison.
Heh, I know about the curling up. That was a slight exaggeration which I hoped to be humorous.
And, indeed, you wouldn't get a single crossbowman shooting in battle, but all the same, a single knight would not charge either.
Wellllll, only in so far as a lethal weapon can be hoity toity stylistic ponce pieces, sure. One peasant with one crossbow would not be all too much threat versus a knight, however. Now, a pro with a pro crossbow is a slightly different matter. If he can keep his cool.
In Britain all of the warring kings agreed to ban the crossbow because the bolt would punch through the armour like it was tinfoil. I assure you, ballistic weapons were the end of the knight. (Even the broadhead arrow would can-opener it's way through some good plate).
Think about it. Training and armouring a knight was ludicriously expensive. Give a few plebs a crossbow and show them how to aim and all it takes is one shot to kill, and even less of a shot to wound, maim and cripple. What about if his horse goes down? Try moving fast in plate vs some peasants in cloth. You are a sitting duck.
I'm going to have ask for a good source on that. Not in the least because you said "all the warring kings" and that brings to mind the seven kingdoms period. Rather before the crossbow came in widespread use.
I do however recall a certain Papal bull which you might mean instead. This bull is commonly said to have prohibited crossbows, but it also prohibited the use of bows
against fellow Christians because the Pope felt it gave too much of an advantage to peasants over nobles. Suffice to say, no lord much bothered with that particular papal bull because they knew they could lose a very distinct advantage. (Just picture that, you take the bull to heart and ban all ranged weaponry from your army and then march into a foe's land who promptly hires a bunch of mercenary crossbowmen to thoroughly annoy your forces)
But yeah, err, I'm rambling again. You, Wannazzaki, are right that crossbows can be dangerous to heavy armour, but you really want a crossbowman who can stand and aim properly when a heavy cavalry charge is approaching
and you want a sufficiently heavy crossbow. A light hunting crossbow, for example, can be pulled by someone just holding it down with their foot and then pulling the string. A shot from that would not kill a plate-armoured horseman. An arbalest or a heavy windlass crossbow on the other hand, would have a much better chance.
Hence why mercenary crossbowmen were reviled by (lower) nobles but still saw very common employ in the later middle ages.
Ehm, I have to add that I can't actually
find the attempted ban/bull in question. Perhaps it did not exist.
Edit; about sitting duck; a knight would not be much slower than a peasant, a knight in full equipment (roughly 30 kg, yeah) would still manage a decent turn of speed because they would have trained with heavy armour and athletics for years if not decades.