In the behind-the-scenes-doc the writers and producers discussed the layers they were looking for in Kirk. He needed to be an iconoclast and a badass, as well as have "command authority". Everyone who read for the part, they claimed, could only do one or the other, not both-- except for Pine. The only hint we see of that side of him is in his exchange with Uhura after sitting in captain's chair and later when he tells Sulu to fire on the ship even the they're still on board. So, that side of him has been seen already, its just very fleeting. I could see him mourning the loss of a redshirt in the next movie.