Well, one of the maxims of war is that there is a use for any weapon, it just takes the right commander to find it. Fighters would have uses in Star Trek, but only those an armed shuttle would have...namely, ground support, recon, and close-in attack. As was shown in one episode of STTNG, launching fighters against a starship that can see them coming and has nothing else to worry about is a futile effort, as the starship has enough spare firepower to sweep them all aside without even slowing down (as the Enterprise demonstrated while the crew were under alien control).

Against such a target, you need another ship able to occupy the starship while the fighters move into their range, or have the ability to hide them until they are in effective range. At that point, the massed firepower of the fighters will actually exceed that of a starship, and can result in crippling damage before the target is aware of what's happened. The downside is that, should the attack fail to cripple the ship, or the fighters are seen before they can fire, the fighters will be doomed. For this reason, I think it's more than likely that a large part of the fighter designs seen in STO are stealth and ECM equipment to throw off enemy targeting systems, which is why they require a carrier to haul them around....all that gear means a warp drive that is probably extremely short-ranged and/or short duration. Unlike a standard shuttlecraft or runabout, a fighter would probably only be able to maintain warp speed for a few minutes.

Anyway, that's my take on it.