The basic idea is that we can enjoy both the prime universe and the alternate one together as explained in Parallels, and we do not need any fixing. Anyhow: 22 minutes sitcom style? No thank you ... That would turn me away from the series. And all this continuity fixing, and reusing as homages footage from previous series you really think it would have an audience that would sustain Star Trek in TV? I think for the casual audience it would be just confusing and they would turn away ...
That's one problem with hardcore fans of any franchise: they assume that it should be written for them, so when they
write something, they write for themselves and people like them. Only, studios aren't interested in that. If you really want to make a series for Star Trek fans, maybe you should do a web-based thing like New Voyages, but forget the mass media.
And about the alternate timelines thing, yeah, it doesn't need fixing. Explain it as you wish: alternate reality, writer error, retcon, split timeline, etc. But in the end, the writers chose to reboot and do something new, and I don't expect we'll ever get back to the "prime" timeline, nor do I think we should. Sometimes you just need a clean slate.