A fighter carrier in this environment is just plain silly, though the idea of "parasite craft" docked to the outside of the ship Suliban-style would work extremely well.
No matter how the fighters were attatched to the ship is it not still a carrier?
In space craft, you could dock fifty fighters to the belly of a garbage scow and call it a carrier; in that sense, yes, there are probably some carriers floating around. As for "space craft designed specifically to launch and deploy fighters," that's just a waste of resources.
Because the whole point of a shuttle bay is a secure enclosure where shuttlecraft can load/unload personnel and equipment and have maintenance done. A fighter small enough to fit in a starship wouldn't load or unload anything except munitions and a pilot and the maintenance could be carried out in a conventional shuttlebay (see "Space Above and Beyond" for an example of a really efficient space fighter carrier; the fighters dock with the ship and both the cockpit and weapons stations are serviced by waldos).Besides, a shuttle bay works pretty well, why coudn't a ship house fighters and launch from that platform?
The main reason is that any starship big enough to be useful as a fighter won't be small enough to fit inside a shuttlebay. A Klingon Bird of Prey doesn't need to land between missions.Not sure why it's "silly".