I don't think those missiles are quite powerful enough to blow an entire continuity away.
You'd be surprised. Continuity is a delicate thing.
Just ask Daniels.
Besides, how is such a viewpoint capable of handling such things as the coexistence of the Mirror Universe with the Prime?
The simple fact that mirror universe isn't continuous with the prime universe. It's PARALLEL to it, which means they do not actually intersect, and historical events in one universe do not affect the other.
What's interesting is that the Mirror Universe is VERY similar to the Prime Universe in that the same people and locations can be found in both universes and they otherwise lead fairly similar lives. There's Good Kirk and Evil Kirk; there's good Sulu and Evil Sulu; in the 24th century Evil Kira is a Bajoran despot running a slave labor camp and Worf is a Klingon warlord with a humongous battleship. So at least by trek rules, a parallel universe can run side by side with another universe in a lot of interesting ways even if the two universes never directly influence one another.
Which means the Abramsverse probably would have turned out HISTORICALLY identical to the TOS universe if not for Nero's arrival; Enterprise would be three times as large and Number One would look like Ashley Judd, but Christopher Pike (whose hair color has changed in this timeline) still would have visited Talos-IV, still would have met Vina, still would have gotten irradiated and confined to a bleeping wheelchair until NuKirk and NuSpock took him back to Talos-IV.
And somewhere out there in the multiverse is apparently a version of reality where Winona Kirk had a daughter instead of a son...
And, once again, it was never expected to.
It was until Nero showed up, apparently.
Although, in light of the many time travel events that could not have logically happened in the Abramsverse, I'm still strongly of the opinion that Nero's actions affected the timeline in BOTH directions, past and future. The same thing happened when the Enterprise-C arrived in the -D's era: Captain Garret arrived in a future in which the Klingons and the Federation had been a war for decades. In the same way, Nero's actions would/should have created a timeline where the Borg never invaded 21st century Earth, Gary Seven never intervened in the militarization of space, and Zephram Cochrane didn't need anyone's help on his first warp flight.