Mildly stupid question: Are carriers a thing in Star Trek?
Yes, but no, but also yes.
In strict canon? No.
In background intended materials? Yes.
In non-canon games and such? Yes.
The Akira was designed as a carrier. We never saw it USED like that, but the design was. There's a few from games.
The Galaxy could function as one, in background materials. The shuttle bay is supposed to be an entire deck and fill out the middle of the saucer.
I don't think a carrier is outlandish for Starfleet, but Starfleet shies away from military-focused ships in general. A carrier would probably have to justify itself as having a dual non-combat role, like for disaster support and evacuation or something of the nature.
Small craft seem to be of limited use in Trek overall. Capital ships are essentially just as maneuverable as a fighter would be. DS9 used Miranda's and such as "Fighters".
EDIT -
I counter with rather than a carrier for small craft, a fairly monumental project of something like a mobile starbase. A vessel that can enter a sector and function as a sector hub, with starbase-level medical, repair and fabrication facilities. Have a few smaller, Defiant-scale craft permanently attached to it.