Why would he? He'd have to go back to 2233, which would change the lives of countless billions of people not directly involved in Vulcans destruction.
point about time travel as depicted in Trek I think is valid. In ST IV Spock makes the process look easy. In fact he makes the computations in his head to achieve time travel.
The second major time in at least film, is the Borg use it as a way to stop the federation from being founded. If they failed the first time why not try again - and again - and again?
Part of the problem with time travel throughout all of the series is if it is as simple as it appears why wouldn't they use it more frequently to save billions of people?
Generally speaking as a plot device I think Time Travel scenarios suck because of all of the holes it creates in the narrative.