I always considered fighters in Star Trek as something that keeps getting tried on occasion but then usually discarded for the same reason, in that the return of investment isn't there. In the case of Star Trek, I doubt you could put enough oomph into a one-man craft to seriously threaten a good-sized Starship.
In-universe, I could see these things having a niche application as a system patrol craft, customs enforcement and that sort of thing. When the Dominion war broke out, the Federation was insanely desperate and pulled in everything that had a phaser equipped.
From an entirely subjective, personal standpoint, I like Star Trek better without fighters being a thing. It fits better with the format, it fits better with the episodic and large-cast nature of the story-telling in the various shows. Therefore, when I play in the verse, there are not going to be any.
I agree with all of the above, and at the same time, I am not surprised fighters would exist in the Trekverse. They would be niche warships/aircraft, specialised for very particular military duties. For most battles, bigger ships are much better and more useful. You'd have lightly armed mostly utilitarian shuttles (the majority of small craft), hybrid solutions between a shuttle and a fighter, and least common of all, dedicated fightercraft.
If plenty of non-Federation factions and powers do have various fightercraft, it would be a bit shortsighted if the Federation never had any at all. Instead, I think it's sensible to say the UFP always has some fighters prepared just in case, but for most common exploratory, military and diplomatic duties, large well-armed ships and more lightly armed or unarmed small craft are the everyday mainstay. Particularly in times of peace, where there isn't much need for greater variety in military spacecraft.
Here's the lads from Trekyards talking about canon and non-canon fiction examples of fighters from
Trek. Mostly Federation stuff.
A look at the Cardassian
Hideki type of large fighter.
The Lore Reloaded fellow has more to say about this too. As all three of them state clearly, the setting is better off without prominent and common use of fightercraft, as it seems to fit the logic and tone of the setting better.
Personally, the thing I like about fighers in
Trek, whether they are Federation or non-Federation, is that they are at least proportioned reasonably. Most of the fighters, even the smaller ones, are actually pretty big. The Federation's
Peregrine (or whatever it's called) is about as big or almost as big as the runabout, and that's a big and hardy multi-purpose shuttle in and of itself. The alien fighters, such as the Hideki discussed above, are similarly big, or even a bit bigger. The Maquis raiders, mostly converted spaceplane freighters and transport ships, are in that ball park too. About the only fairly small fightercraft we see on a regular basis are the Bajoran fighters and raiders, as those really are just up-gunned shuttles or aircraft/scoutship hybrids for planets and local space. I'd say the likes of Voyager's Delta Flyer fit neatly into the hybrid solution category - yes, it's just a medium-sized shuttle, but if you need to use it as an emergency fighter, you can. Neither an entirely defenceless shuttle, nor a dedicated fighter.
In the case of entirely local powers, such as the Bajorans, or regional powers, such as the Cardassians, fightercraft do actually make a lot of economic sense. Particularly for the Bajorans and later for the Maquis, since they had little in the way of larger dedicated ships. When you look at the
Bajoran fleet inventory after the occupation ended and they liberated their system from the Cardies,
they didn't exactly have that much to work with, so reliance on whatever surviving or converted fighters they had - seemingly the most plentiful military spacecraft left - doesn't suddenly seem so weird. For a few years after the end of the occupation and without Federation help, rebuilding a basic fleet no doubt took time and they also had to deal with reestablishing a civilian merchant marine (astrine ?) during the early rebuilding period. (They have a well-running one in the later seasons of
DS9, so civilian and military fleet rebuilding was definitely going on, as much as their situation allowed them at that time.) Finally, there's the fact that a not insubstantial part of the post-occupation Bajoran fleet seem to be freighter ships armed to act as impromptu warships. (Amusingly, a very medieval, as well as WWI and WWII era concept.) From what I remember, some of those converted freighter models looked like Cardassian ships on purpose ! Indicating that these were salvaged and captured Cardassian ships, modified with Bajoran tech and given Bajoran colours, and then sent into service.
I think it's no surprise fighters are seen most often in
DS9, as their appearances there make the most astropolitical and military sense. Then you have the occassional cases in
Voyager and
Enterprise when the main cast runs into some aliens of the week who sometimes have their own types of fighters, often for defensive or even piratical duties. Overall, though, fighters aren't that overexposed in
Trek, and that's a good thing in my book ! One of the things I find a little annoying in the
Star Wars universe is that the fighters are so small and there's almost an overabundance of specific types. They're cute fighters, but even less realistic than Trek's soft-but-hard-enough fightercraft tech.
I'd say a strange but unique halfway point between fighters and other large ships would be multi-purpose smaller warships designed like large spaceplanes. The Klingon Birds of Prey are an obvious example, but one of the few larger and purpose-built post-occupation Bajoran warships, the winged "assault ship", also shares this design philosophy. You can use it as a planetary transport and very large gunship in an atmosphere, and as a fairly speedy and nimble (though weaker) warship while out in space. A
Galaxy class ship could blast them out of the void with relative ease, they'd have to get creative to defeat one, but they are big enough to go toe-to-toe with many medium-sized Federation and other alien ships. I think if the Bajorans in particular had to fight a few Cardassian cruisers (
Galor class, etc.) and neither side had fighter support for the big ships, they'd probably use those winged assault ships and a few of the converted, armed freighters they have in their fleet after the occupation. Bajor was only slowly rebuilding their fleet after the occupation and if they lost those BOP-like assault spaceplanes of their's , they'd be down to armed freighters and their various fightercraft and shuttles. (That's one thing I arguably like about Bajor and its ships. They really feel like they have a cobbled-together inventory of whatever still works, and they're at the doorstep of pondering whether to join a major power, the Federation. Me coming from a small country that didn't join NATO that long ago and still has a lot of work left to modernize its inventory, I've always had sympathy for the Bajorans in this area. They're just working with what they've got.)
Here's the scene from season 7 where Kira's aboard one of the assault ships, part of a smaller fleet that tries to force the Romulans to stand down.