I'm not sure of the rationale behind not having fighters in Trek, because from a tactical standpoint it would seem to be the superior method of interstellar battle (multiple attack vectors, minimized casualties, etc)...
I believe the rational for no fighters in the Trek Universe is that the larger capital ships have higher warp potential than the smaller craft, there seems to be economies of scale that allow those large ships to reach those higher warp numbers than is possible for smaller craft, that is why my fighter uses an alternate power plant than the typical Matter/Antimatter design....
Well, don't forget that there were
fighters in Trek, albeit not seen until part way through the Dominion War. My personal speculation as to why they didn't appear earlier is that it wasn't until then that technology could be made compact enough to make such a small vessel into an effective combatant. Maybe a spin off from the development of runabouts.