Sometimes overall strategy requires that designers include things that make no tactical sense for the object being designed. This was very true in the case of submarines during the Cold War. People have always had an interest in adding unusual items to sub designs. The British M.1 featured an enormous gun as one would find on surface warships. The German "Deutschland" was a modified design of U-Boat with enormous cargo space, used for trade with the U.S. before the latter's entry into WW1. And, of course, there was the very popular idea of using subs as aircraft carriers (which everyone tried from time to time in the early 1900s).
(Most of these were simply mobile seaplane garages (such as the French Surcouf), whereas others were full-fledged carriers with direct onboard launch capability. Carriers included the British M.2 and various Japanese efforts, such as the I-15 Class (aka the B1-type), though these always featured single planes. (However, the B1-type I-25's single plane conducted the only known aerial bombing of the continental U.S.)
There was also the huge I-400 class capable of carrying and launching three planes. However, I discount the I-400 since it was not so much an aircraft carrier as it was a kamikaze-guided-missile carrier, intended for use in a suicide attack against the Panama Canal.)
However, only the addition of nuclear weapons really took off.
Whereas the other additions might still be useful, however, the nukes aren't considered to be in the modern climate. And so some have wondered what to do with a large number of perfectly operable submarines that just happen to be excessively long so as to contain a number of upright tubes.
Well, The Skunk Works has figured something out. A small UAV is ejected from the sub's tubes and allowed to float to the surface, where it launches. After performing recon or attacks, it returns and somehow executes a non-destructive water landing, at which point it is recovered.
This is amusing on several levels. First, that thing looks like an F-86 Sabre and an F4U Corsair made babies. Second, the idea of a sub-launched airplane just has a note of irony that can't be ignored. Third, there's the fact that the dream of a proper submarine aircraft carrier could be realized, with a small fleet of aircraft able to be launched while the sub remains cloaked underwater. And finally, of course, there's the fact that weapons capable of destroying a city are being replaced with weapons intended to blow up trucks and buildings.
Advancements, after all, come in many forms, and sometimes in directions opposite what one might expect.
In any case, it's interesting that none of the major cloaking races of Trek make use of similar ideas. "Balance of Terror"[TOS1] was a sub-hunter analog, after all, and given that we've seen fighters in Trek (albeit usually in the form of "miniature" starships of almost a hundred feet long) we know the two could be mixed.
If we continue the sub/cloak analogy, it seems to me that the Klingon emphasis on individual glory could easily have resulted in the use of cloaked fighter-carriers instead of their reliance on small independent cloaking warships such as the Bird of Prey. However, apparently the ease of adding cloaking devices to BoP designs made that the more attractive option . . . not to mention that all the warriors would want to be pilots instead of manning the cowardly "hiding" carrier.
This leaves us with the Romulans. Surely they would man a hiding carrier, and given their weapons technology they could probably have created a devastating fighter in the 2260's. Presumably the technology simply never advanced to a point where they felt they could get away with it.
After all, radar pretty much killed the sub advantage during WW2. It wasn't until sub reactor advances allowed for constant submergence that subs could realistically be hidden again . . . but then there was sonar. The point, though, is that if a sub surfaced to launch a plane . . . a plane that would probably be small and short-range in the first place . . . then as soon as the plane was high enough to be seen on radar the location of the sub would be known.
Similarly, the early Romulan holo-cloaks of the 2150's made the ships difficult to spot, but still easy to track. 100 years later, they were still detectable as a 'motion blip' via unclear means. So, if you were a cloaked Romulan carrier, you'd have had to have cruised to a location without being detected, launched from outside detection range, and then pick up whatever fighters returned (and hope they didn't bring company).
In short, the idea seems neat, but may be problematic. Sure, something similar is the basis of the Yorktown/Minotaur combo at the Starfleet Museum, but we're talking about the use of such tactics in a different sort of 'reality' altogether.
More thought would be required to make this workable, assuming it could even be practical.