Yep, he fell through a plot hole. Almost wish they had just called it a remake/reboot, instead of tying it to the old continuity. Doing it this way requires Spock to forget the 50 other times he's been stuck in alternate universes/timelines, and all the ways he knows to repair them/get home.
Yes, it's a different timeline, rather than a changed timeline, so he doesn't HAVE to go home, but it smacks of something similar to suicide to not try to go home. If you say it doesn't matter because it's a different timeline, and exists seperately as another of many alternate universes, won't matter if he "repairs" it, as it'll continue to happen as another probability wave anyway, won't it?
All he had to do was go back to the point the Nerada appears in this universe and blow it up, and only change to this universe is a strange sensor reading on the Kelvin. Instead, he gives up on HIS universe and decides to stay and play in this alternate sandbox.
Yes, needed all of this from a RL standpoint, keep this universe and don't reset things, but including Prime Spock, but ignoring how many times in his life he's overcome basically this same problem, is silly.