The "carrier-trained" bit only has to do with how long the unit sits on the carrier, and has nothing to do with pilot training. You can plop a unit with zero planes and zero pilots in it onto a carrier, sit it in drydock, and in 90 days it will be "carrier-trained."
Sad as it flies (pun intended) in the face of reality. This is one area where the game's attempt to emulate "realism" falls way short.
It is not so much the game fault, although there are issues with the game engine for this "feature" to be more representative of real world practicalities, but rather player abuse of the feature. Without the abuse the abstraction works to a satisfactory level.
A very serious code rewrite would be necessary to make the player abuse impossible to achieve. Things which would need to be considered in any rewrite would be:
1. Making individual pilot accreditation for carrier operation, as well as the current unit and aircraft model, mandatory. This could be as "simple" as having a pilot toggle or as detailed as creating a new pilot skill. Either option opens up a Pandora box of additional coding.
(a) to be consistent with the existing pilot training which serves as a simplistic accreditation abstract, the toggle/skill must be obtainable by training a rookie pilot. However having gone down this path of "realism", to be consistent this training would have to be limited to onboard carrier training only. Allowing an accredited air unit to be moved to land for training just opens it up to abuse too easily
(b) to be consistent why wouldn't float plane pilots embarked (and their respective air units) not also be required to adhere to the same standard of being accredited to conduct ship operations. That then leads to issues with float plane units/pilots which were never qualified for such operation.
2. Out in the real world, pilot accreditation is not a once obtained and forget process, it requires regular exercise of the skill to maintain that accreditation. Thus AE would need code to make it possible for both the air unit itself and each indivi8dual pilot to lose carrier accreditation if they fail to operate off a carrier for any extended period. As it currently takes a continuous 90 days to get a "Carrier Capable" air unit upgraded to "Carrier Trained" status, a starting position would be 90 days off sees reversion back to only "Carrier Capable" status. Something similar for pilots. However coding this (which requires new tracking), without opening up several obvious "cheats" is difficult. Still, a successful coding effort would stop absolutely the current player abuse.
3. Once we start down this road of pilot accreditation in an attempt to make the game more realistic, the coders would have to look at aircraft crew size. Those concerned about the existing abstraction, never seem concerned that a B-29 has a game crew of only 1 (aka a sole pilot). Surely to be consistent it (the same applies to the 4E Japanese patrol planes) should use up to 10 "pilots" as it's crew. Fortunately the code already has a hook in place to accommodate different size crews to operate the different aircraft models. Still, even with this hook, a lot of coding would still be necessary and integrating it with the current skill training system as well as the current pilot replacement quantums is tricky.
4. Operational and training accident rates would have to be substantially increased. Overall training mishaps were very deliberately toned, and quite significantly at that too, in AE because player protests were too strong in classical WITP (and they were much less there than out in the real world). It is a common feature of this series of games that those who most criticise the gap between the abstraction and the real world praxis are the first to complain when their wishes are met. Imagine the outcry if there was a 20% training mishap rate (not necessarily resulting in pilot death or a total airframe writeoff) whilst the air unit/pilot was getting their carrier operation accreditation. Another issue here would be the effect of leader stats and how it would modify these operational and training mishaps. Also would different aircraft models impact on the accident rates. As always, once you start tinkering with the code, it is always a much bigger exercise than the punters are prepared to acknowledge.
It really would be much easier if players just didn't abuse the feature.