But let us be serious for a moment here...
When Kirk fired that torpedo at an unshielded impulse exhaust port, he should've had no doubt that it would be a crippling blow (which we see as there are explosions in multiple parts of the ship). The design itself was a decade plus old at least, one of Starfleet's best engineers got the chance to study one up close and personal for three months and it's likely that Starfleet retrieved the remains of the one Kirk crashed into the bay and gave it careful study.
Anyone arguing that one Kirk's "fire everything" is anymore respectable than anothers is simply deluding themselves.
Of course, that's not what the audience would want to see.
Funny, I didn't find it particularly bloodthirsty behavior by Kirk, at all. Time was of the essence, and the obstacle needed to be removed quickly. Remember, the scene cuts back and forth between the battle and the assassin preparing to shoot as the president gives his speech.
I found Spock's reaction to Kirk offering to rescue Nero and his men far more out of character and bloodthirsty than the things Kirk did that are being discussed here.
In TUC, I'd think any surviving Klingons would've destroyed themselves and the ship rather than face the dishonor of surrender, anyway (and Kirk and Sulu probably knew that). After all, that's what the Romulans did in "Balance of Terror" after Kirk offered to rescue their survivors.