In fairness to Pine, he was given the task of playing Kirk on his first space assignment, cocky and untempered by experience, whereas Shatner's Kirk was played as an experienced veteran who had seen the wonders and horrors of space up close for years.
On that first day Kirk had to deal with an enemy/threat who:
Was from 129 years in the future.
Had advanced weaponry and technology.
Had already destroyed a plant and killed it's 6 billion inhabitants.
Had destroyed 5 starfleet ships.
I don't think Shatner Kirk had to deal with anything matching such scope and magnitude. The closest things I can think of would be The Doomsday Machine, and the events of TUC.
Pine Kirk made a judgment call to permanently end the threat Nero posed. That's his responsibility as a captain. Pine Kirk did extend an olive branch before destroying the Narada and Nero smacked his hand away. Despite all Nero had done; including kill his (James T. Kirk's) father. Pine Kirk was attempting to find peace with the Romulans.
Shatner Kirk had no qualms about firing on General Chang's ship in TUC. He didn't treat Khan and his people on the Reliant with kid gloves either. All the shots to area surrounding Reliant's bridge affirm that. Then there are all the Klingons Kirk killed in TSFS. By self-destruct of the Enterprise and by kicking them off a cliff in to a river of lava.
No matter the universe.
KIRK GIVES NO QUARTER TO THOSE WHO CROSS HIM.
I'm not sure what that has to do with my post about how Pine was told to play the character; dealing with this all for the first time. Just because he had a really bad day doesn't mean he's instantly acquired years worth of experience in processing those thoughts and emotions. What comes off as a blase aloofness could simply be a lack of knowing the seriousness of what's to come and understanding the consequences of your decisions based on years of processing past actions.
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.
Into Darkness has the same problem. Spock, pushed past his breaking point, is clearly trying to murder Khan, not apprehend him. That makes sense, actually, and it's a reminder of the pre-Surakian savagery that lurks in all Vulcans, not just he half-human ones. It also underscores just how deep his brotherly love for Kirk runs and just how fragile watching his mother and his home planet die has left him, a year or so on. And then, before he can take it too far and cross a line he would have a tough time living with himself for crossing, Uhura stops him. Again, so far so good.
But her rationale? "He's our only chance to save Kirk!" (And why couldn't any of the other superpopsicles--products of the same gene manipulation and selective breeding--have done the same?) Pretty selfish, you ask me.
I think your argument would be stronger if Spock himself had not spent much of the film's second act talking about how a mission to assassinate Khan would be a clear violation of the law and basic morality. The film had already established that killing Khan is a bad thing; it doesn't need to beat us over the head with it.
I'm sorry, but you (and the movie) seem to be missing something. Spock abandons his principles out of understandable but ultimately selfish reasons only to stop not because he remembers what he stands for but because he;s given an even better selfish reason to let Khan live. If Kirk's resurrection wasn't on the table, would Spock then have a motive not to kill Khan?
That is my entire point: the film ultimately lack the courage of its convictions. And yes, in this age of water boarding and drone strikes, the audience does need to be beaten over the head, as unfortunate a turn of phrase that may be.
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.