I really liked Carol in STID, and they actually added to her character in that movie. She and Kirk had an attraction, that is obvious, and she's on the Enterprise now. They've set it up perfectly for a future romance. I agree that seeing Kirk and Carol actually DEVELOP a relationship would be something new. If David eventually comes along, then Kirk seeing his son grow up and not meeting him for the first time when he was already grown up would also be something new. It would also further this Kirk maturation story that's been present in both of the films.
I think I'd like that too.