The strength of the new movie franchise is in its characterisation (except Scotty IMO because he is just to much of a departure). I could give a pass to Kirk on your analysis if there was some indication that it was a brutal decision based emotion and inexperience except that Spock is baying for blood up there with him and he gets a massive reward for his actions. They both have reasons to want to kill but Spectre of the Gun rears its head again. They failed the test. I think they were trying to back-pedal after the first movie to try and underscore that Kirk's arrogance and self-belief are not always good things. The way you succeed is as important as the success. I am perfectly happy with Spock losing it, since it is not portrayed in a positive light. I'm less happy with Kirk's brutality against his prisoner earlier in the movie while standing next to several other officers. Police officers would be prosecuted if one of their prisoners took a beating like that after surrendering. However, I am willing to give Uhura some credit. She knows Spock. She knows why he's gone berserk and she knows that it will be hard to reason with him so she personalises her pitch to make it specific to the cause of his grief. It's smart and Uhura is smart. It also justifies sending her down instead of just a security team, although her AND a security team would have made more sense.