If we melee with a bow, i would expect to take increased damage to it. but really i feel this is not needed. punching makes a lot more sense than striking with a bow.
it's fine in movies and what not. but reality is you can only do this with certain kinds of bows or you wont' have a bow that shoots arrows anymore. and the bow has to be specifically designed for this.
Any composite bow may work for this. because they are typically a bit more durable. but self bows or compound bows are a lot more fragile. but really any bow not specifically designed to be used in melee shouldn't be used in melee. a punch makes 200% more sense.
Given this is a game i wont' complain either way
stabbing with an arrow also is fine though.