Yup, I'm a tremendous advocate of the possibility of a Shatnerverse extension into amateur fanon. Just to see him mentor a younger officer (sort of like his grouchy persona on "Shit My Dad Says",) and/or finally die a plausible death of old age or a sudden affliction like a heart attack or brain aneurism or both, that has (little to nothing) to do with off-world / off-ship intrigue.
One day, Kirk's first officer comes to his quarters with a typical first-responder team you'd expect to be assigned to a VIP. He's there to retrieve Kirk for ship's business...only to enter Kirk's quarters via a security over-ride code. Upon entering Kirk's quarters, sees Kirk laying there with an obvious deceased person's quiet thousand yard stare in his bed.