The issue with the idea of fighters being effective, cheap, but highly risky combat units is that it just explains why the federation eschews them.
The Federation does not eschew them. They've used them in multiple engagements during the Dominion War.
Sacrifice of Angels
SISKO: Forget the Klingons. Our job is to get to Deep Space Nine and prevent the Dominion reinforcements from coming through the wormhole, and that's what we're going to do. Attack fighters, tactical pattern Theta. Concentrate your fire on the Cardassian ships, and then split off into squadrons and run like hell.
NOG: Why is he only targeting the Cardassian ships?
GARAK: He's hoping to get them to break formation and so they'll after the Federation fighters. He knows the Jem'Hadar will stand their ground, but the Cardassians just might get angry enough to take the bait.
NOG: Attack fighters in Theta formation. Cruiser and Galaxy wings at half impulse.
SISKO: Sisko to attack fighters. Prepare to engage on my command.
BASHIR: You should listen to him, Ensign. He's a professional.
SISKO: Attack fighters full impulse. Fire at will.
O'BRIEN: They're not taking the bait.
SISKO: Ensign, send in the second wave. Tell them to keep targeting the Cardassians.
NOG: Aye, sir. Second wave on its way. Third and fourth waves on hot standby.
SISKO: Mister O'Brien, have Destroyer units two and six move in closer. They need more cover fire. And tell Captains Diego and Reynolds to stay alert. They may try to outflank us.
DAMAR: I'll say this for Captain Sisko, he is persistent. That's the ninth wave of Federation fighters he's sent against us.
DUKAT: Well, his persistence is about to pay off. Let's give him his reward, shall we? Have a half dozen squadrons break formation and go after those fighters.
DAMAR: Yes, sir.
SISKO: The Magellan and the Venture are supposed to be protecting our starboard flanks. They're in too tight. Ensign, tell fighter squadrons six, seven and eight to...
NOG: Sir, I can't get through to anybody. Communications are down.
Not only were fighters seen and mentioned, but they played a pivotal role in Sisko's strategy in baiting the Cardassians.
It does not explain why everyone else does. The Dominion has zero regard for the lives of its soldiers and ample resources, but doesn't have fighters, instead flavoring a mix of very heavy capships back by larger swarms of light warships.
You're misinformed.
A Jem'Hadar fighter, or Jem'Hadar attack ship, was a small type of warship that formed the bulk of the Dominion fleet. These versatile starships were also known to perform the roles of patrol ships and scout ships. Jem'Hadar fighters were vaguely insectoid shaped, looking much like a Terran...
memory-alpha.fandom.com
That small ship that the Dominion likes to swarm with? They're classified as fighters. The TM classifies it as a strike fighter. And yes, they're also classified as fighters in the show. At least once and supposedly from time to time.
The Die is Cast
LOVOK: What type of ships?
PILOT: Jem'Hadar fighters.
TAIN: How many? I asked you a question.
PILOT: One hundred fifty.
TAIN: Tactical display on screen.
It should be noted that the Cardassian Hideki is also classified as a fighter in the script for Sacrifice of Angels, though on screen it was mentioned as a shuttle (but that's because the design was recycled, much like the Peregrine fighter itself).
the Klingons, with a warrior ethos that heavily values personal success as a warrior and value death in battle, don't field fighters, even though fighter pilots are infamously prone to becoming glory hound egomaniacs due to the nature of the role, which sounds like it would fit the Klingon mindset quite well.
There is irrefutable proof that ST has fighters. In literal dialogue from multiple episodes, where they're pivotal to actions that the heroes are taking. And going by its size and function, I suspect that the Klingon BOP occupies much the same position as other fighters. It's just a more supped up version.
As to why the confusion exists, it seems to me that the fighters in the setting occupy a sort of hybrid function. That of a patrol/fighter craft. And each power has a sort of balance on how they lean towards one or the other function. For the Federation, they seem to be more primarily used as fighter or courier roles. It's not worth keeping even a small frigate around to protect a small colony, but a squadron or two of fighters? Not only would the economic burden be little more than supplying a shuttlecraft (of which everyone seems to have plenty of) while providing the ability to patrol within the system's reach. Consider pirates and mercenaries. Also consider that one outfit in TNG was bold enough to even attack what amounts to a para-military science facility.
The Dominion and the Cardassians tend to make use of their fighters in a more patrol function, with limited roles as fighters. The Cardassians primarily due to cost and resources, are better off with moderate size patrol craft that can keep their dominated worlds in check. The Dominion, being so vast in size and capability, greatly benefits from having smaller patrol craft that can deploy troops and perform key strikes, but both need to retain greater mobility than you might find on a capital ship.
The Klingons are the farthest away--so much so that it's more like a scout ship that might occasionally take on fighter roles. They can patrol, move in small squadrons, and perform more long-range missions as a patrol craft, but are also generally the ones to take on roles that in today's world, would be mostly attributed with stealth fighters.
EDIT
Between the visuals of the squadrons in the show and the fact that Sisko sent 9 waves, with at least 4 waves being different waves (ie, first wave sent, second following, three and four on standby) and assuming there were ONLY four per wave, you'd get at least 192 fighters. If each wave was in fact, a fresh new wave, it jumps to 432 fighters. And that's only really assuming one group per wave. If Sisko sent say, two groups per wave, those numbers double, so the number of fighters that Sisko used to bait the Cardassians could be between 384-864 fighters, but were at least 192-432 fighters, depending on how you want to frame it.
SECOND EDIT
It should also be noted that "fighters" in space are not really a sound strategic ploy in large scale fleet engagements. Modern fighters are used because we have a horizon over which ships cannot accurately hit their targets. And so fighters were an answer to that limited range; cross the distance with small little weapon platforms that deliver near-battleship firepower to the enemy.
In space, where most of the area is empty, fighters as we understand them don't really pose much of an advantage. It's cheaper and safer to use use drones and missiles instead.
Hence, ST fighters being a cross between courier/scout/fighter makes sense. It's the only way that they can really be competitive in their environment.
THIRD EDIT
We probably shouldn't get too hung up on visuals specifics, because this is the same show where they regularly had deflector dishes firing phaser/disruptor cannons throughout the series from the ship models and never bothering to stop. Which is really funny, because all those models had actual guns on them.
FOURTH EDIT
Upon further thought, the Federation had deployed 600 ships to the battle. There are two ways you can take that.
First, you might assume that the fighters were not a part of the ship count. In which case, you'd probably expect that if a military force deployed 600 capital ships, they probably deployed thousands of fighters.
Second, you might presume that the fighters were part of the count. Indeed, the LUG sources suggest that this is the case. It would therefore be illogical to assume that the Federation deployed more capital ships than fighters, going by simple economics of production, in which case you might have 432 fighters and 168 capital ships.
In which case, we might assume similar numbers for everyone else. The Dominion fleet would be primarily composed of 72% fighters (which I mean, looks right regardless), presuming that the Dominion *only* supplied 1/3rd of their military force towards the end of the war (and it's probably closer to 2/3rds) you would get 7,200 fighters and 2,800 capital ships.
In either case, during Operation Return, you would have say 903 fighters for the Dominion and 351 capital ships for the Dominion.
So it was:
UFP
Fighters: 432
Capital Ships: 168
Dominion
Fighters: 903
Capital Ships: 351
Might explain why after the Klingons arrived and took out several capital ships, that the battle itself began to turn against the Dominion. Because even though the fighter count was astronomically in favor of the Dominion, the absolute difference between capital ships was not so high. Especially when you might consider that it looked like a more or less even split between the Cardassian and Dominion capital ships--and Sisko's waves of fighters had routinely targeted those same ships. Which are outdated and behind Dominion and Federation ships.
So, something worth considering.