As I said earlier, Spock "fixing" the timeline would essentially murder Kirk and replace him with the TOS version, alter the last 25 years of trillions of people and condemn Romulus and Remus to death in 2387.
Spock is not god. He doesn't have the right. STXIKirk has the same right to live as TOS Kirk had. The damage was already done by the time Spock arrived in the past.
All Spock could do was minimize further damage.
Hmm. As opposed to the countless number wiped out by erasing the TOS timeline?
But it doesn't matter because the TOS timeline wasn't wiped out because the Abramsverse isn't the original.