A major theme of TWOK was that Kirk was feeling old. We know that Kirk was actually a couple of years younger than Shatner, and Shatner was barely 50 when they filmed TWOK -- hardly old for a ship's captain. Now, obviously, this gives an actor a lot to work with, so I'm sure Shatner didn't mind, but did they overplay this element?
I think the age concern was valid for a Kirk who--as McCoy observed:
This is about you flying a goddamn computer console when you wanna be out there hopping Galaxies.
For the
job he may not have been too old, but being out of the field for so long made him feel useless. Its often a contradiction of reality, but sitting around-doing not much of anything can make one feel tired (instead of content or refreshed), or old, while exerting yourself, pursuing your life's goal makes you feel alive.
Spock adds this insightful line:
If I may be so bold, it was a mistake for you to accept promotion. Commanding a starship is your first best destiny. Anything else is a waste of material.
Take away a man's reason to be, and he will wither--even if he's successful in other fields. In Kirk's case, he was promoted to admiral, but that was just a title with no heart--not the reason he joined Starfleet. With his reason to be far removed from his life, his calendar age would seem to gain his attention, as he was just another older officer collecting dust, instead of being an explorer challenging his life over and again.