It strikes me as pretty unfair to put this limitation on bow users when melee characters need only buy a sword once and be able to use it forever with no maintenance or limitations. Same with a wizard and buying a spell scroll. They now have that spell forever and, of it is a cantrip, can cast it as many times as they like.
Limited arrows just nerfs the physical ranged builds of the game by saying they can't actually use their primary weapon at all times. Alternatively, if there is enough ammo everywhere that they can use the weapon at all times, then the mechanic becomes pointless or just an extra punishment in the form of additional carry weight.
The only games where I like ammo management are survival games or franchises like Fallout where scavenging for ammo is a part of the world and franchise. And even then it can be really frustrating when you buy a bunch of 10mm bullets for your pistol and head out to fight something big just to get hit by a random deathclaw attack, blow all your 10mm ammo, and have to go back to hopefully buy more.