There's an issue with multiple ships firing too many missiles vs an unshielded target, yeah. This is addressed in the dev version.
Missiles I think would work well with infinite ammo, with minimal changes:
Swarmers, Annihilators (both), Locust, Squall
The main issue there is flux cost. They'd end up being far too good over a long battle. As they are now, they're a limited amount of flux-free pressure a ship can exert, with various wrinkles. If they have unlimited ammo, they become both overpowered and boring - from something that's an interesting decision to fire, to something you literally never want to take off autofire.
It could all be worked around, perhaps, but a solution would have to address those concerns. IIRC I tried this with Swarmers a while back and it really did feel awful, they went from "a fun thing to fire" to a "have to make sure I'm firing them on every cooldown" chore.
The main issue I have with limited-ammo weapons is that, in some cases, they distort the optimal player tactic to one of 'wait out enemy ammunition, then engage'. The most egregious example here is an Onslaught with four Annihilator Pods - as long as it's got ammo for those, it's very hard to push an engagement - due to both the flux-free damage output, and the fact that a wall of annihilator rockets tends to absorb a large portion of incoming attacks.
So, for example, I would not suggest just removing ammo from the Annihilator pods like you did with salamanders; instead, I'd suggest dropping them to maybe 30 shots and making them regenerate that in chunks of 20. (Exact numbers subject to gameplay testing.) That way, if you pressure a target using them, there'll be an initial burst of damage, and then you'll start to get large openings where it can't keep firing, followed by another burst of damage.
And that's a design that shouldn't distort player use too much, either, since 'wait for ammo to regenerate' wouldn't translate to backing off for too long.
* * * *
From a player perspective:
* Swarmers: Like Thaago, I use them in small battles, and do generally just put them on autofire there; swarmers are fun, but they don't pack enough punch to be worth triggering myself. If I had a swarmer with regenerating ammo... I'd still just put it on autofire, but I'd also be willing to use it in larger engagements.
* Harpoons: The racks are good; the pods are not. I'll often put racks on small ships to give them a bit more punch to exploit enemy openings; the pods, by contrast, are meh - if I want punch for a medium missile slot, I'll go with torpedos, which are punchier, have more shots, and are less likely to get wasted against unimportant targets. Some form of ammo regen for the pods wouldn't be a bad idea (possibly along with a salvo size reduction), but I'd leave the racks alone.
* Sabots: Again, the racks are good... except that if you give them to the AI, they won't use them effectively. Pods are, again, meh. So sabots basically only come up if I'm personally piloting a ship with small missile slots; this tends not to happen after the early game. (I -could- put sabots on my Aurora... but why would I do that when I can mount more ion cannons instead and not have to worry about ammo at all? Hm. I should still test this, though; having an extra 12 sabot missiles might be more useful.)
I don't think you can currently do this without modding it in via combat plugin, but I think the fix for the three-shot sabot racks would be to add in a relatively slow regen (maybe one shot every 20 seconds or something?) that can only restore ammo from zero back up to one. That way you can't pull out of combat and build up another huge alpha-strike launch, but AI ships that waste their sabots will get another chance eventually.
* Squalls: Have the same problem as annihilator pods - the best player tactic is to wait out enemy ammo. Maybe a solution like I suggested for sabot racks would work, where it regenerates back up to a max of one salvo's worth?
* MIRV: Two of these on a Conquest is pretty good; they function like guided torpedos. Without regen, though, it's hard to justify spending the ordnance points on these, and I frequently end up fielding conquest variants that are either entirely missile-free or only mount salamanders. Perhaps if its heavy weapons integration mod applied to missile mounts (perhaps even large and medium) as well as large ballistics?
* Locust: I've tried these and never been much impressed. Like swarmers, this is one of the first missile mounts I'd toss ammo regen on.