Leave him dead and have Kirk return to be Captain of a ship. But that's not the III we got and the outcome makes him extremely arrogant from that point on....
This is a tenative peace, a fragile affair. Spock opened the door and let a bull in the china shop. That's how he put the mission in danger.
I'm not following your arguments because I don't understand Kirk was arrogant or endangered the Kitohmer mission. You haven't really explained either of those. Especially since you said 99% of fleet captains would be no different than Kirk.
Kirk is both arrogant in IV, V, and VI (as a character) AND he endangered the mission by being such an overt bigot and moping around the Enterprise. He wasn't vigilant against possible attacks on the ship. He was drinking Romulan Ale and calling Chang Hitler. Enough examples?
Why an outlaw Kirk? I don't know. Why not? We've seen him every other way, but mostly as the good, if not rough around the edges, soldier. This is a new facet of Kirk and it shows what he;s willing to do for friendship. I don't see where arrogance shows up here. Just fierce loyalty. You need to give me some examples.
Because he sacrificed his career for his friend. Fine. But take away his career. Don't reward him. The man doesn't do anything he doesn't want to do for the rest of the movies. He complains. He doesn't report back to space-dock. He is a renegade, emboldened by what happened with Spock. His attitude toward the Klingons adds to this. They are the only ones he hasn't vanquished.
"We've done our bit for King and Country."