Yeahhhhh..... NO. Arrows would become too easy to obtain, and if we had the right bow, we could easily kill everything if we had that many arrows.
Use a looting III sword. Use an Infinity bow. I suggest you write to Mojang then :/ You can do that by going to Mojang.com and getting their email.
That would be wrong. Lets say I have 200 skellies in my spawner mob trap. I move with in firing range and they all fire at me. So there are now 100+ arrows stuck in the ground. Lather, rinse, repeat.
Lets say I have a redstone contraption. It pushes me around every 3 seconds. I have a skeleton farm in front of me. I go afk, the skeletons shoot and miss me, I get infinite arrows. I could also just use projectile protection armor.