I suppose we'd be looking at it differently if it had been McCoy or spock they'd killed.
I'm sure. But it's like towards the end of Galileo 7, Uhura said they saved 5 but not who and Kirk is just soooooo relieved, not any concern, yeah, 5 out of 7 ain't bad but it's like he knows the two aren't Spock, Scott, or McCoy.
And Kirk actually does spend some time staring down at the dust from his crew person.
I notice often when a show is willing to make it's audience a bit uncomfortable, it tends to be more effective. Not everything is safe and easy. Just because the officers aren't all in black and playing mournful music doesn't mean no one cared about her.