OTOH, it's rather amusing to think that godlike intellect and powers are just random occurrences, like some sort of nasty infections you get from a broken toilet seat... Puts us intelligence-worshipping monkeys in our place, really.
You know that. But Kirk didn't think of it.
I can't really see Kirk first calmly arranging for Mitchell's ultimate destruction via radiation bombardment, and then succumbing to red haze and deciding that he absolutely needed to punch him in the jaw as well... "He had to be stopped, period!" would be no rationale or excuse for going after him, not unless Kirk had become utterly deranged.
On the other hand, "He had to be stopped, ellipsis and question mark" would
be. Perhaps reason and mercy still stand a chance of working? Nothing will be lost by trying, except of course for Kirk's own life.