I'm not responsible for the opinions of others
I'm not holding you responsible for the opinions of other. I'm observing that you basically argued that Kirk's reaction to Kirk's death is implausible because you
would be more torn up by the death of a coworker than by the death of the biological child you never wanted and don't have. But...
The impression I got about Garrovick, who I believe was briefly considered as a recurring character, is that this is the kind of man Kirk would choose to be a father-figure for, not just because of the debt to the father, but because of the foolhardy courage the kid demonstrates.
What David demonstrates does not impress me, not in either film, even if SFS tries to say he does things like Kirk, because David simply does not register dramatically. Geez, opening day in San Jose, the crowd applauded everybody in the opening credits (even Robin Curtis, who nobody had seen), but when Buttrick's name came up ... silence, followed by a burst of laughter at the silence. What could you do BUT kill a non-entity like that?
I don't know why you're considering the view invalid because of my own personal choices. I haven't killed anybody with my own hands, even people who deserve it, but that doesn't stop me from endorsing some of the actions of Dexter, Dirty Harry and countless other fictional creations who apply a fascist mindset while doing their fictional worlds a favor by ridding them of what I could charitably describe as sub-human trash.