> peasants armed and trained with knight-killing longbows

The longbow's reputation as a hard-counter to heavy cavalry is, I think, a little context dependent. The famous set pieces like Poitiers, Agincourt, Crecy all featured favorable terrain - and in the case of Agincourt, favorable weather - ideal for massed fire into predictable funnels (where, strictly speaking, the longbow served first and foremost as a horse killer).

All this to say, it's IMO a mischaracterization to imply the peasants in the aforementioned peasants revolt held the military edge relative to the crown and its allies. After the initial shock of the uprising, they were a clear underdog matched against a well resourced and ruthless opponent.