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.
To me this way you are arguing the point really speaks to how weak the premise of the pic must be, that it all hinges on 'idiot plotting' requiring a major character to be inactive in the exact kind of situation he would NEVER be inactive.
If SubPrimeSpock is really a changed character with age, one content to live with the new timeline
or however you describe it (I'm not wanting to hear the quantum universes thing, that is TNG much more than TOS and I don't give a crap about TNG), then the movie should have been about what changed his perspective, which is a huge switch from the character I know of.
And anybody messing with time would have to be that 'arrogant' ... or perhaps another word would be in order there. Maybe if the situation was a Jewish person who could do something back in time that would might save 6 million jews from camp deaths and the like ... would he be arrogant to risk however many other millions? Prob'ly, but that wouldn't invalidate his choice in the slightest.