As for causing more damage to the timeline... the planet Vulcan, 47 Klingon warships and six (or seven? don't recall) Starfleet ships have been destroyed... hard to muck things up worse than that. Not to mention the possible future that's now been created... one possibility is a rapid militarization of the Federation and the Klingon and Romulan empires... or the Romulans deciding to attack when they discover the Federation has been weakened by Nero's attack (and is in fact now missing one of its key planets and all its resources).
If it were me, Earth had been destroyed, and I had Spock's intelligence and capabilities... you bet your britches I'd be slingshotting around the nearest star/heading to the Guardian of Forever ASAP.
Then you would be one arrogant person to dictate how the lives of god knows how many people should turn out, I mean yes Spock normally tries to "fix" the timeline but he may have realized that there is know way of knowing what trying to fix it will do, yes it could return to normal or it could cause the Kelvin to be lost with all hands including James T. Kirk that would pretty much fuck things up, or Nero could get away to Romulan space without the damage the Kelvin inflicted by ramming it.
Plus even if the old timeline is erased then the Prime universe still exists unless it never occured to the people complaning about the history change can't accept the fact that according to Star Trek's own multiverse rules there must exist a universe exactly the same as the prime universe EXCEPT that Spock and Nero were not pulled into the black hole.
Commas are your friend.
There's no real evidence that this timeline exists alongside the old one, but we've been over this already.
I'm not suggesting that they do what I'm talking about in the next film. I think it would be silly to do so. I'm just saying it's something Spock would do, given his behavior in prior Trek. That's part of what makes the whole time travel aspect of the film somewhat detracting in my opinion.
As for putting Baby Kirk in danger, etc, you could distract the Kelvin with a phone distress call beforehand... none of this is the point, however.