But this does not preclude accepting the events of TNG, DS9, VOY and ENT as canon. Just that we want a new storytelling style.
I think that you have to simply let all that go. I want the next show-runner to have total freedom to place the show in the 28th century with the Eugenics Wars happening in the 23rd and the first warp flight happening in the 25th, if he/she so desires.
Carrying over continuity from the old series would just shackle the new creative team to something that has nothing more to offer creatively.
In that case, why bother to call it Star Trek?
Because Star Trek is more than just forty years of continuity. It's a concept--and sometimes a set of characters--that aren't necessarily tied to the particulars of what happened in a previous cycle of TV shows or movies.
You can make a STAR TREK movie or TV series, about the crew of the Starship Enterprise
exploring strange new worlds and all that, without having to, say, stick to exactly
what "Balance of Terror" said about the Romulan Wars. That was the old version. Doesn't mean you can make a new one.
Just like you can make a Sherlock Holmes movie without being wedded to the continuity of the old Basil Rathbone movies or whatever. Or you can make, say, a Mission: Impossible
movie that doesn't necessarily treat every old TV episode as "canon."
Star Trek does not
have to incorporate the "prime timeline" to be recognizable as Star Trek. Trek is an idea, not a trivia contest.