Oh, that's trivial. Kirk is not a real person, he's a collection of people depicted by non-likeminded writers. Any and all morals are present there for that reason - 78 episodes is plenty enough for that.
As for personal ailments, I tend to find myself disgusted by people who not only mistake TOS for a progressive and liberal show, but argue that the ultraconservative values displayed therein define progressive and liberal in any context. Ridiculing the open militarism of the show is a healthy antidote to that, at least for my half of the problem.
Finally got to see the movie, BTW. And yes, it does appear as if there's a S31 agent or sympathizer aboard every Starfleet ship there, making it quite plausible that these would stumble onto Khan eventually.