Yes, most English peasants were expected to practice archery. While it was not a legal requirement to have access to a weapon, the fact that you could be pressed into military service meant that it was sensible.

From the position of the upper class, that doesn't always seem like a smart idea.

I'm doing some guesswork here, but I'm guessing that your logic is that all the weapons lying about makes a peasant revolt much easier?

A peasants revolt was much rarer in England than you would think. Rebellions did not become commonplace until after the black death. When one third of the workforce was wiped out, labour became in much higher demand which lead to workers revolting for higher wages and better treatment.

From the point of view of a medieval baron. You held much more power if you could field more soldiers, so having a rabble of peasants armed made sense. In the unlikely event of them turning on you, you were fairly safe in your castle and a small team of armored professionals was more than capable of defending you.

Shoot, British != English. Sorry about that ._.