Why wouldn't Spock at least try to return to the prime universe?
He has a (maybe still) wife, also perhaps children. Aside from the personal aspects he is the Federation ambassador to Romulas, with the massive destruction to the empire caused by the supernova, Spock will be needed more than ever. Spock has always been shown to be a very responsible person. It not like he wouldn't be able to come up with something. Just skip from one universe to another.
1. Either he can't, based on whatever law of quantum mechanics is in play here (i.e. he can go forward in the future, but it will be the future of this new alternate universe), so he is forced to stay in this one instead;
2. He has the ability to return to the prime universe somehow but has elected of his own free will to stay in this one instead; or
3. He has the ability to return to the prime universe somehow and has every intention of doing so as soon as he helps the Vulcans of this new universe settle on a new world.
The movie heavily implies that the first option is what happened.