I typically don't main an archer in TES, but let me assure you that in most RPG's I primarily play an archer, it fits my play style well.
If arrows aren't unlimited I will find very quickly a way to make that an arbitrary limitation.
There are about 3 or so games that made this not very possible:
Dynasty Warriors 2-4: I could hold what, like 20 arrows?
and
Assasins Creed
Aside from that I will assure you I would go to any ridiculous lengths necessary to "spray amd pray" with my arrows.
-example-
In Dungeons and Dragons I wanted to play a ranged paladin. Eventually I realized I could summon my horse/ horses gear 1/day. so I would load up my Horse with all the weight he could carry in arrows. At this point he pretty much had armor made of quivers for arrows, (and typically I would fire 8-16/ round)
-Video Game Example-
In Tes, with Arrows being free weight, any time I would go to any store I would just purchase their entire stock of arrows. The amount of gold I was spending in it was negligible, because the weight is free, and I knew I would use them at SOME point. Eventually I would have pages and pages of arrows of all varieties, and I would never fear running out. Even if it weighs SOMETHING, no one in their right minds would make it weigh TOO much, and if Stam still ups Carry Capacity, then you bet yer ass my Archer will have really high stamina.
Trust me unlimited arrows MAKES things a fair fight. If they think that having arrows be in limited supply helps to BALANCE ranged combat, then that simply means Ranged combat is comparatively overpowered, and that quite arbitrary restriction of "have arrows" will easily be overcame. If it weighs something, you bet my inventory will be little else than a smattering of potions, the two bows I wanna use, and 30 arrows for every one of those two thousand mother [censored] running around Cyrodil 