When I say "alive" I am not contrasting him with characters in other directors' works, just Nolan's. I'd say Nolan's films tend to be unemotional, sterile, lifeless in a lot of ways. Prestige was huge fun but the main characters were unexpressive, lifeless. I'd say the default for a movie character is "alive" and Nolan's previous characters fall short of that (apart from Memento, as I stated).
As far as showing and not telling, I think the movie shows Coop's emotions a *lot*. We aren't told that he's unhappy about leaving Murph, we see it and hear it in his tone, in his desperation to make a connection before he leaves, in his tears. That's not "telling."
When we see him react to the playback, there's nobody saying "boy, you sure seem upset about this."
When he's in the tesserract, we see his desperation and pain for it to end differently. TARS doesn't say "you seem to be upset, not that your life is ending, that you made these choices and desperately want to reverse them."
Yeah, he may explain some stuff a bit at times, but I don't see that as a general problem with Coop's emotional state.
Contrast with Inception, where we are told repeatedly that he wants to get back to his kids, but I don't think I ever *felt* that once in that movie.
The ending is a cheat, and a weakness of the film, IMHO, that wants to have all the connection stuff resolved and move on to a hopeful, space-exploring future. I agree it's an off note and could just has easily been a scene where he's spent a week with her and she says "what's next" and he runs off. But it doesn't change the fact that for 2.5 hours prior we have the most fleshed-out human character in a Nolan film maybe ever.