Kirk was prepared to rescue Nero and his crew and he took Spock's rejection of the offer as a chance to execute Nero.
Or a chance to end the most dangerous villain the world had ever seen. You are insisting on viewing this a certain way.
Also: Spock just lost BILLIONS of his kin. If you don't think this is going to affect your decisions, I don't know what to tell you.
And the idea that a theatre of people would give up a rousing cheer over the execution of a foe that's been rendered helpless makes me wonder just what they feel.
They feel it's a MOVIE with a rousing ending for the villain.
Please don't try to conflate that with anything pertaining to reality. I laughed my ass off when I saw Hannibal Lecter show us a guy's exposed brain and eating it, in the second Lecter movie. I wouldn't find it funny in real life.