Those who like time travel "back to the future" style can still assume that quantum mechanics doesn't contradict that and, therefore, kelvin trek is another universe because a black hole was involved (and there are already theories about black holes being access points to different universes).
There is no evidence the creative team had ever wanted to rewrite tos and eliminate prime. They always said the opposite.
I think it was smart. In a way, it works just fine with the merger too, now. Had them rewritten tos with the old time travel device, or through the usual remake, it would probably be the end of this trek now because their version would conflict with TV trek.
But the way it is now, it doesn't conflict. They can co-exist. They created another reality that you can ALWAYS use for different stories. They simply made the trek universe bigger.
There is no conflict between TV trek and the movies right now.
Imagine the black hole having two sides, one is prime and the other is kelvin. The Picard show will make us see what happened in prime after the destruction of Romulus and Spock's disappearance, while the movies give us a look into that "other side" and thus where Spock prime went when he traveled through the black hole.
The reason why Spock prime doesn't go back to his reality is given in the movie: because he makes his mission to help the vulcans of this reality rebuild their world (further because young Spock can be more free to continue his career in starfleet)
Home is relative for him at this point of his life, and trying to get back to his reality would mean having to find a way to create or get to the black hole that can selectively access to his reality. He'd need a technology he doesn't have or cannot use because it might have risks he isn't willing to take. Besides, who is to say he'd WANT to get back? If he has nothing to come back to, it may not be worth it. Maybe he was content ending his life here, to help the vulcans, to see the possibilities...maybe he even got the chance to know his father better through kelvin Sarek.
When he volunteered for that mission to save Romulus it was a suicide mission, he knew he had little chances to come back. The fact he ended up into the kelvin universe and still managed to make himself useful, to have a new purpose, was a plus.