Therin of Andor wrote:
He knows the slingshot trick. He used it to save Earth from the whale probe.
Check out the recent novel, "DTI: Forgotten History" by Christopher L Bennett. The USS Enterprise's engines were subtlely altered by their first (accidental) time travel (in "The Naked Time"), permitting a certain ease of use ("Assignment Earth", etc) - and the slingshot trick replicated later, in a Klingon vessel (ST IV), was extremely risky.
In any case, he'd be saving the Vulcan in this new timeline. The Vulcan of the prime universe is still there where it belongs.
Do you want him to save Amanda, too? Kirk's father? Chief Engineer Olsen? Cadets who get killed in the movie? Where is the cut-off? All the characters probably have dead relatives they'd like him to return.
ToA, you took the words right out of my mouth. If there are questions WRT time travel and it's effects or why don't we just do this or this - I wholeheartedly recommend reading both of Christopher L Bennett's DTI books. He does a very good job of reconciling a lot of questions.