I think Mirror, Mirror is safe - in a sense. Spock knows he must send Kirk and an away team to the MU in order to make contact with MU Spock and help overthrown the Terran Empire, except this time hopefully not just making room for a Klingon-Bajoran-Cardassian empire to take over instead.
Hmm, that one's actually gonna be pretty tricky to pull off, even knowing the future. So Old Spock will change the plotline by arranging the journey, but not as an accident, and planning strategy for it in advance, while briefing Kirk, Uhura, McCoy and Scotty on what to expect - if that's even the right team to send through - anyone but Spock is possible.
Or, conversely, send Spock thru alone, and that way MU Spock will become your "prisoner." What better way to convince him than to show him how logical your universe is in comparison to his?
Regardless of what they try, who knows what the impact might be? They can make their best guess and just see how it turns out.
However, none of this "wipes out" the parallel, Prime timeline. Its not like a standard time travel episode. In those episodes, we're worried about timeline pollution, etc. But here, we have time travel PLUS travel into a parallel universe. So the old timeline is intact.
So I guess my question really is, what stories might we see in this new reality? Anything but the ones that we know Spock can already solve.
...and it's possible that all
Trek time travel stories have also been parallel universe stories.

That's a favorite theory of mine: The gang time travels to the past, which unbeknownst to them, is the past of a different reality (because it's impossible to travel w/n your own timeline, to avoid the grandfather paradox). They change something by accident, and fear for their own future. So they fix what they changed, return to their own time/reality, and phew! Everything's ok again. Except it was never in danger!
And that's the way it does have to happen because if you changed your own past, you could never repair the timeline exactly as it had been, any more than you can unscramble an egg.