I’m not sure he was an “Academy Admiral” in TWOK. I figure he was still Chief of StarFleet Operations, this was simply the class he was mentoring.
I used to think that Kirk became the Commandant of Starfleet Academy between TMP and TWOK, but now I think that he either went back to being the Chief of Starfleet Operations or some similarly dull desk job. He's not terribly familiar with any of the cadets in TWOK outside of Spock's protégé Saavik and Scotty's nephew Peter Preston, both of whom he's presumably met before from the way he teases them. He asks Spock how his cadets will
really react under pressure and is initially inclined to dismiss them as "children." Plus, if Kirk was actively involved in teaching cadets, I don't think he'd be as burned out and depressed as we see him at the beginning of TWOK.
All of this leads me to think that Kirk coming in to rate Spock's cadets, inspect the
Enterprise, and join them for a three-week training cruise was a special, one-time event, and a part of Kirk's birthday celebration. He wasn't typically involved in the day-to-day of any of that stuff, but Spock and McCoy obviously picked up on the fact that their friend was hurting, and enlisted Sulu, Scotty, and Uhura to help them cheer Kirk up. (Chekov, being on the top secret mission of finding a suitable planet for the Genesis experiment, wasn't able to join and probably wasn't even able to receive a communiqué from Spock or McCoy.)
This is all one reason I really enjoyed Christopher Bennett's "The Higher Frontier". It's a post TMP story that goes with the idea that Kirk commanded the Enterprise for a number of years after TMP. And it covers how and why he took a promotion to Admiral yet again. He gets the Enterprise assigned to trainee duty, encourages Spock to take a promotion to captain and this stint as Admiral would be different than the last. First he would not be chief of Starfleet operations, so he won't be a 'desk-bound' paper pusher. He was made Commandant of Starfleet Academy this time. And he would also be a troubleshooter. When problems arise he would take the Enterprise on missions, with Spock as captain, and take care of problems as they arose.
That's pretty much what my friend Glenn Greenberg did in his
Star Trek: The Untold Voyages mini series from Marvel Comics in 1998.
Novels go in that direction because they seem to think it is more interesting than telling stories about Kirk behind a desk. For me, I see no reason Kirk didn't continue as Chief of Starfleet Operations right up to TWOK. And that "we'll give you special missions, just take this promotion" comes from "The Lost Years" series of books, IIRC.
Yeah, the "Troubleshooter" concept comes from J.M. Dillard's
The Lost Years, although it doesn't jibe with Decker's line in TMP about Kirk not logging a single star hour in the last 2 1/2 years. Again, I think in the world of ST, Kirk didn't have a terribly interesting career between TOS and TMP, and for much of the gap between TMP and TWOK.
But what a missed opportunity for a celebrity cameo!
STVI
already had celebrity cameos.