Agreed. In The Final Voyage, he just accepts his promotion like nothing happened, despite his well-known dislike for a desk job.
That gets me wondering. Was it ever really overtly stated in TOS that Kirk had a dislike for desk jobs? Yes, in "The Deadly Years" he showed disdain for a "chair-bound paper-pusher," but he wasn't quite himself at the time. And just because, as a line commander, he was often impatient with the decisions of the people back home giving him orders, that doesn't necessarily translate to an unwillingness to accept promotion to a position of greater authority. Lots of people grumble about their bosses but then accept promotion to the same positions when it comes their way.
I think that, like many "well-known" qualities ascribed to Kirk, this disdain may be something that was established more in the movies,
after he'd been in a desk job and decided he didn't like it. And it was the novelization of TMP, not any canonical work, that introduced the idea that he had to be manipulated or tricked into taking a promotion.
I just did a keyword search through Chakoteya's TOS transcript site, and I find no instances in TOS of Kirk ever saying anything to the effect that he was unwilling to take a promotion or a desk job. The phrase "desk job" never appears in TOS at all.
So I don't think there's enough evidence in TOS
per se to conclude that he would've been particularly resistant to taking a promotion to the admiralty or would've needed some special incentive for it. It could be that he simply didn't have a problem with taking a promotion at the time, that he was tired after five years out there and wanted a break, and that after a couple of years at a desk, he decided he'd made a terrible mistake and
from then on had a problem with the idea of a desk job. So I think a "final mission" story that has Kirk just accepting the promotion without any special reason for it is just as valid as one that shows him resistant to promotion and needing a special reason. There's nothing in canon to rule out either approach.