Let's just admit the scene was what it was....
A deliberate and knowing attempt to thumb their nose at what Abrams likely thought were the boring 'moralistic crap' he didn't like about TOS. I admit to pure speculation here based on Abrams stated dislike of TOS. It was an attempt to say, 'Hey, no boring morals and deeper meaning here! Dude pissed us off, dude gotta die!'
To put it in Trek perspective: THIS Kirk would have moved right to kicking Kruge into the lava pit. There would have been no attempt to save him first.