The Shadow of the Demon lord system is different and interesting. You don’t track individual arrows, you track quivers (which are quite expensive). A character might have like 3 quivers.
You lose a quiver on a critical fail, otherwise you don’t track ammo. This means on average you have 20 arrows per quiver, which works out about right without any of the paperwork.
Interesting but i don’t like it from a role playing angle. I don’t know how to explain how that works, but if i could it would be cool.
Not a player myself, but would this work?
Each quiver holds a single arrow, but they are enchanted with a replenishment function. If the archer utters a specific phrase just after drawing, the arrow replenishes. If they miss the very tight window, the enchantment is broken and has to be re-applied.