Those blunt weapons were designed against armor, if bows were effective melee weapons then why would they feel the need to develop warhammers and maces? Why not equip everyone with longbows? They got range and and work as blunt weapons! Or maybe not.
Besides, 200 pounds isn't really that much if you compare it too the force of common blows. The average boxer hits for 700-1300 pounds, if you hit someone with a bow with that force it would most definitely bend, and if it doesn't bend then you're not hitting hard enough, either way, you wouldn't be dazing or injuring someone. You're more likely damaging you bow, sure it wouldnt shatter into little pieces, but it certainly wouldn't be healthy for it. And like you said, its their most effective weapon on the battlefield, why risk it when you have other weapons at your disposal, weapons meant for melee combat?
Im sure someone, somewhere, managed to save themselves using their bow to hit someone, just as some old lady used her purse to fend of a mugger on occasion. Would you buy a purse for self defense? Probably not.