One of the notes does actually address this point:

23 At the battle of Courtrai, for instance, the small principality of Flanders was able to muster an army of archers larger than the army of the entire kingdom of France, which consisted of knights and men-at-arms (Rogers 1993, p. 252). In this sense, a weapon like the longbow allows for the military enfranchisement of commoners, which institutionally constrains the ruler

It doesn't go on to discuss this further, but it shows that while maintaining a large force of archers required a population widely practiced in archery, where a region could muster enough longbows it enabled them to effectively combat the central control of their country.