Seeing as Spock is apparently shell shocked or suffering from PTSD for the remainer of the movie, why would he be allowed to not only ship out with the Enterprise but be named First Officer? He encouraged Kirk to fire on the Romulans even though they no longer posed a threat.
"Captain, what are you doing?
You show them compassion, may be the only way to earn peace with Romulus.
It's logic Spock, thought you'd like that.
No, not really. Not this time."
Even when Kirk says it may be the only way to earn peace with the Romulans, Spock chooses revenge.