I don't have trouble with Spock's reaction (his home planet was just destroyed and his mother died in front of him).
Right, so you are saying he was still "emotionally compromised" and shouldn't have been on duty?
IF I were inclined to nitpick, I might object to Kirk's actions, but my Star Trek nitpicking days are long gone.
Is that even possible?
But I guess you are saying, when it comes to fictional material at least, nothing is important.