If they served no real purpose as a consumable, there's no reason to keep them. By purpose I mean:

*Various effects or damage types based on equipped ammo.
*A reason to switch or conserve ammo for a particular weapon (not even a factor in this game, more so in shooters)

The current arrows serve no real purpose. What's the difference between using arrows right now and a proposed system of not using arrows? One less item to carry around. That's it.

Going from a lore perspective, that's an entirely different issue. Though over time I've come to realize that not everything in a game needs a precise explanation and often trying to explain some things just makes it more confusing than leaving it to the imagination. As long as it is consistent and the game world itself treats the game mechanic like it should be there, there's no problem with it in my eyes.