How does Vulcan matter at all? The survivors from Vulcan set up a colony on a new planet. Now tell any story you want involving Vulcan and it doesn't matter if it's the original Vulcan or New Vulcan. Aesthetic differences have 0 baring on the story being told and will likely be different than either JJTrek or PrimeTrek. Unless you have desperate need for canon porn any story that can be told in one universe can be told in any other universe, the only people that care about the universe are small number of fans complaining on internet message boards.
To play devil's advocate here: The universe ("prime" or "JJ") absolutely matters. For the fans.
That's the reason why J.K. Rowlings new books all take place in the Potter-universe, and not some unrelated wizard world. The reason why the Star Wars prequel made so much money is because it's the same Star Wars setting. If you are already interested in something, it's much easier for people to get excited about more of it. Something like "brand recognition" exists. Hell, I watched "Ant-Man" in cinemas, purely because it's part of the Marvel cinematic universe. I wouldn't have bothered otherwise.
That's a deeply personal connection that everyone has to decide on it's own on. I cared for Sam Raimi's "Spider-man". But I didn't care for Marc Webbs "The Amazing Spider-Man". It's a completely new, different entity for me, despite having the words "Spider-Man" in the title. And an inferiour at that.
In the same vein I care for the "Star Trek" universe. The main one. The new JJverse is a completely different entity for me. One that has yet to persuade me. If the new show is set in the JJverse, it will need to win me over the same way a completely unrelated sci-fi series would need to. I would watch it with the same level of interest as I watched the first episode of "The Expanse" or "Dark Matter", with the exact same probability of me just switching off, if it hasn't won me over after the second episode. If it's set in the "prime" universe on the other hand, I'm already guaranteed to watch it, and willing to support it even if it's mixed/bad in the beginning, the same way I watched all the other Trek shows, because I care so much for this universe and am willing to forgive more mistakes.
That's just my sentiment though (albeit one apparently shared by some other fans). If it's enough for you for something to have the words "Star Trek" in the title (and see for example no difference between "Spider-Man" and "The amazing Spider-Man") there's nothing wrong with it. It's just my personal sentiment that's different.