I see your point too, Horatio.
Indeed....in certain situations (as we may recall in "Balance of Terror") Kirk did say something along the lines of "in order to preserve the peace, this ship and crew are considered expendable".
That same logic/mentality could probably have been applied to the scenario portrayed in the new movie, but, there is one important caveat, set forth by Nero himself. "I do not speak for the Empire. We stand apart." Therefore, it was not a matter of Federation and Empire (pardon the titular license)
Granted, Kirk did not have all the available info to know for sure exactly what Nero's crew might have been intending at that crossroads moment, but, I don't think that's a chance he would've wanted to take. Erring on the side of caution, Kirk protected his own. Spock made his objection plain, but, it was Nero who held the final nail in the coffin, not just for himself, but for his crew. Kirk simply wielded the hammer.
Besides that, Kirk also had his homeworld to think about. Nero escaped from the Klingons. He could probably easily escape from the Federation were he to be captured, tried and convicted with imprisonment, and then become (somehow) an even bigger threat. I'd dare say that even in Kirk's mind, when he offered mercy and assistance to Nero and crew, he probably thought: "What the hell am I doing?" When Nero declined in his very adamant way, Kirk was cleared of all further thought into the matter, and went to option two.
BTW, Kirk, it would seem in this movie, is about the same age as Kirk Prime when he took command of the Enterprise. After all, both Kirks are (as far as we know) the youngest officers ever to take command of a vessel, especially a capital ship of such renown as the Enterprise.