I don't really see it as being as much of an issue as the OP suggests. Fighter spam is subject to the same limitations as several other things (like torp spam): it doesn't scale infinitely. One carrier is good. Three carriers are great. 30 carriers are going to get blown up by an equivalent-DP fleet from a serious opponent. Higher-end ships are stronger defensively against fighter spam, have better PD, and tend to have more fighter coverage themselves. Fighters will rip through low-tier trash when massed, but against massed good direct-fire ships they can't keep the enemy battle line off of the carriers without a good chunk of the fleet being direct-combat itself.
At most I'd suggest a few more variants with more OP allocated towards PD.
(This is entirely ignoring that carrier spam is the most boring, passive way to play and I can't imagine anyone enjoying it for very long.)
I wonder how would giving all fighters ammo, thus requiring that they periodically return to carriers and give their targets a breather, affect this issue. Has anyone tried it?
This is functionally what fighters themselves are; the "reload" is the time it takes for the ship to produce new ones after they get blown up.
I disagree with this just because some of those guns are really great fighter killing weapons. The current plasma cannon has a tag to stop if from firing at fighters on autofire and perhaps that tag could be shared to a few more guns, but for the most part medium and (sometimes large) weapons are excellent tools for killing fighters.
A few are good at killing fighters, but when AI/autofire slowly traverses slow turning guns to waste flux at fighters that they probably won't hit when there's enemy ships nearby it just causes ships to get flux-locked and blasted and in a stupid and frustrating way - both because you lose ships to it and because it's abuseable as all hell against AI. Imagine playing a naval game and battleships randomly turn their main batteries away from enemy surface targets because some fighters are flying by.
There is no justification for this kind of issue to still be in the game after a decade either. Why can't gun groups have target priorities? Why can't ships have target priorities?
Use your targeting key. All non-PD weapons on autofire will prioritize the targeted enemy ship over all other targets so long as its inside their firing arc. Don't leave your important high-flux weapons on autofire. Focused fire is vastly more efficient than letting every weapon fire at will anyways, the only time I wouldn't do it is when there's such a substantial disparity that it doesn't matter, like flying a fully kitted-out Paragon into a cloud of pirate frigates.