The whole "5-year mission" thing is weird to begin with. We see much of it in TOS, and it does not seem to be a five-year-long stretch of deep space research at all. Rather, the ship returns to port every so often, scrambles to perform military and diplomatic missions, and even visits Earth twice. How is this five-year period different from what the ship did during the rest of her existence, then?
It appears that the five years in deep space were an issue only for Kirk himself and his closest officers, not for the ship as such. In the newest movie, Kirk is excited at the prospect of being selected to command this mission, supposedly because nobody has done it before or because it's very rarely done. But why? What's so special about five years, as opposed to, say, two or ten? Five doesn't seem to stretch the capabilities or endurance of the ship at all, and indeed such concerns should be preempted by the frequent port calls.
It might thus well be that five years is exceptional exactly because that's when even the luckiest skippers run out of luck. Technology doesn't help or hinder things much - space simply is too dangerous to be survivable in the long run, and risking five consecutive years is foolhardy, that is, heroic, and thus so appealing to the young nuKirk.
Having the Prime Kirk, a man only slightly older than his nuCounterpart, be the only one to "survive" a five-year mission might in fact be quite realistic. It might even be that he was the only man who ever agreed to performing such a mission... Others would quit while they were ahead, with no loss to Starfleet or science as yet others would continue from where they left off. A five-year mission would simply be a record-breaking stunt, one destined to propel Kirk to fame in a carefully planned Starfleet propaganda move.