People always say the Prime timeline coexists, but that was never actually shown on screen.
I don't see why it should have to be. It should be self-evident that the filmmakers would not want to erase the previous 45 years of Trek continuity from existence. Even if that had been Bad Robot's intent -- which we know from many interviews that it wasn't -- there's no way CBS would've allowed it, because they have too much invested in that history. Even if it's never practical again to make new shows or films in that continuity, the last thing they'd want to do is make it less desirable for audiences to spend money on the DVDs by telling them "Hey, these stories don't 'count' anymore." So it should be self-evident that the original timeline is still as valid as it ever was.
There's also the fact that Pocket, IDW, and Star Trek Online
are still licensed to tell stories set in the Prime timeline, and since tie-ins are obligated to stay consistent with canon, that means the canonical "reality" is that the Prime timeline is still viable.
And what is
shown onscreen is Spock Prime making no effort to "restore" his own timeline, which allows us to infer that he does not consider that timeline to be under threat. Which is consistent with our modern understanding of physics; the coexistence of alternate timelines is simply the more believable interpretation.
So we don't have to see it onscreen to know it's still there. There's simply no reason why it wouldn't
be, and plenty of reasons why it should be.