Captain Robert April wrote:
The Spock from TOS would, immediately upon discovering that he was in a past time period, begin his calculations for a time warp, to get to a point in order to repair whatever damage has occurred and restore the damaged timeline. This Spock does none of that. Logic dictates that this is not the same Spock.
But that would only work if he weren't in an alternate universe that was created when he went back in time. If he were to time warp forward in time, it would be the future of that reality where the Kevlin was attacked, Kirk's dad was killed, Vulcan is destroyed, and in which Biff is corrupt, powerful, and married to your mother.
It's not unreasonable to presume Old Spock knew this (since Young Spock deduced it on his own) and knew it would be futile to try.