Consider that McCoy just finished making the exact OPPOSITE point at the beginning of Wrath of Khan where he urged Kirk "Get back your command! Get it back before you become part of this collection! Before you really grow old!"
But McCoy didn't know of Starfleet's plans to mothball the Enterprise.
Ok, if that's your interpretation of Morrow's actions, fine. But that's a little too overly-complicated for me based on what I saw. Morrow didn't seem to give a shit about Kirk until Kirk started talking about going to Genesis. Morrow stated that it's illegal for anyone to go there, which was true. He then gave Kirk some good advice about not risking his career by doing something stupid while at the same time showing his complete ignorance and total lack of understanding towards one of the founding races of the Federation and their death rites.]I don't think he's trying to spare his feelings either, but I'm pretty sure he's trying to convince Kirk to get the fuck out of that chair and go fly a desk like everyone else wants him to do. I suspect this has a lot less to do with his age or even the age of the Enterprise than it does with Starfleet not really trusting Kirk and wanting to keep him out of trouble.
Let's face it: the Khan fiasco is the snowballing result of a bad decision Kirk made (and evidently didn't properly report to Starfleet, and was made worse by a combination of Kirk's cowboy attitude (not raising shields when he was supposed to) and his personal attachment to Doctor Marcus. Probably more damming is the destruction of Reliant and the detonation of the Genesis Device; the first is just a regrettable loss of material that could be justified by Khan's piracy, but the latter is an unfolding fiasco of which Kirk is the cosmic center.
Basically, they're pulling the "she's too old, Jim" card because it's a plausible way of keeping him the hell away from Genesis before he can make things even worse (and is also why Captain J.T. "By the Book" Esteban got to take David and Saavik on the Genesis Expedition).
More to the point, when Kirk later asks for the Enterprise back, Morrow jumps from one excuse after another (the Enterprise wouldn't stand the pounding! The Council won't like it!) and finally settles on "Think of your career."
That's when Kirk finally gets that Starfleet (or the Council, probably) doesn't want HIM SPECIFICALLY going back to Genesis and Morrow is trying really hard to come up with an excuse. Incidentally, Kirk's return to Genesis wound up creating exactly the kind of interstellar incident everyone was hoping to avoid, although in all fairness it wasn't actually his fault, and in even greater fairness putting him back in charge of a starship probably makes him a lot easier to control since they can now assign him to "Saturn ring patrol" or something until he retires.
I didn't see anything personal in Morrow's remarks, nor did I get the impression that Starfleet was keeping some sort of eye on Kirk. All I saw was some idiot admiral.