First adressing your P.S.: How many they can carry is written in the book, no guessing required.
Also, if your players can't make a simple mark each time they shoot an arrow, they can't track their HP either. Edit: I mean, Monks have to track KI, Spellcasters spell slots and fighters maneuvers, if arrows are too much, those players can not be trusted with any of these other things. EDIT END There are more than a few character sheets flying around with an ammunition tracker on them. Mark how many you have and when you reach that mark, you're out. Easy.
Now to the general matter:
How important or unimportant tracking this is depends on game system and type of campaign.
D&D5 has devalued ranged combat so much by introducing free ranged combat through cantrips that making the archer track their ammunition is somewhat cruel. In the times when spellcasters could only shoot by using a spell slot, magic item, or ranged weapon having "unlimited" ammunition was a huge benefit and was rightly limited to the realm of having a magic quiver.
In other systems where ressource management extends to all equipment and/or were ranged combat is more powerful, the choice of when to use that advantage is interesting and adds depth to an archer character. It also balances out with melee fighters whose armor wears down more when the archer has to restock arrows.
I've happily played in campaings that tracked a lot more things than this, too, and it created quite interesting moments. Especially when it was a choice to use up your arrows and not, like in Star Wars, a roll of the dice that says you run out of ammo.
But to be honest, when you're already leaving out ammo, I'd chuck rations right after. It's as tedious to track and has about as few moments where it becomes important apart from "GM introduces ration loss" as "you run out of ammo".