I agree with this. I think the idea that Spock devised the KM was one of the cleverer concepts in the 2009 movie.
Not with this part, though. I used to think that Kirk was the Academy Commandant in TWOK too, but I've since become convinced that he's not. He doesn't seem to be especially familiar with the students, he at least twice refers to them as
"your cadets" to Spock (emphasis mine), and outright asks Spock how he thinks they'll respond under the pressure of a real mission. All of that indicates to me that he's not really dealing with the students on a regular basis. The only cadet he seems to recognize besides Saavik is Peter Preston, who he might have met years before, the way he did with Sulu's daughter Demora.
Plus there's the fact that Kirk is pretty obviously bored and unfulfilled in his work once again. If he were teaching or running the Academy full time, I bet he'd find that a lot more stimulating than being a deskbound paper pusher. ("Young minds, fresh ideas.") But it seems like Kirk let himself get trapped into a boring desk job once again.
My theory is that most of the old
Enterprise crew aren't normally attached to Kirk's staff or the Academy, and the KM test, the inspection, and the little training cruise on Kirk's old ship are a special reunion that Spock and McCoy arranged for Kirk's birthday. Spock is running the
Enterprise as a trainee ship, McCoy is apparently also regularly attached to the
Enterprise, as his name is
stenciled on the door of sickbay, and Scotty is obviously involved with training the engineering crew. If you believe that deleted scenes are canon, Sulu was scheduled to Captain the
Excelsior. And we know that Chekov became first officer on the
Reliant.
We're not really given any sort of indication as to what Uhura has been doing on a regular basis, though. Maybe she was
already working at the transporter station we saw her at in STIII? Or maybe, considering the way that Kirk just automatically
hands off his book to her when the inspection starts, she was a regular part of Admiral Kirk's staff? His personal attaché, maybe?