For a moment I read the title with "XIII", because I'm actually more interested in seeing the consequences of Kirk being brought back to life via Khan's blood. Seeing the side effects that no one anticipated and showing that the blood is way too complicated to work with thus the Abramsverse has no cure for death.
This! This hast to happen, they have to throw in some caveat in the third movie. But maybe it's a case of letting the genie out of the bottle.
Anyway we had two moments were Bones was worried about Kirk's health, but nothing came of it. Physically Kirk must be fine because Starfleet wouldn't send a captain who is not physically fit enough to complete such an urgent mission. Plus I don't see anything mentally wrong with Kirk, yeah he was pissed off but who wouldn't be after their mentor (and perhaps Pike was a close friend of Kirk's) died?
No those two moments were simply there to give Bones something to do, which for me is disappointing because I would like to see more of JJ (or AU) Bones. The group of scenes surrounding the two scenes where Bone's expresses concern about Kirk's health feel like the ball has been dropped on a lot of things. Act two is full of balls dropping but I guess that's a point of contention for another thread.