This thread has sort of stuck in my craw for a week now and I find myself between DIS episodes and random ventures into Netflix to watch an ENT or DS9 episode here or there thinking about what a brand new, 25th century set, extragalactic Star Trek series would be like.
I actually disagree that it would be the same thing just with new words and aliens. I agree that it would take some radical re-thinking about what science, method, and narrative directions would end up on screen and the sort of "it's just doesn't feel like Trek to me" arguments would be very, very loud if it was done how it should be, but I tend to agree that it might be the best way to go about making a ST series that is set after all that has thus far been made.
From 2100 to 2400 now we've pretty well covered what human exploration of the Milky Way has unfurled for us. I agree that there is alot still unexplored but it also would pose the same challenges and be met with the same resources that every show has seen thus far. I think to do an interesting extragalactic Trek it would mean a MASSIVE ship, a completely rethought timeline of expedition, I'm talking like... the Federation has to find people who are totally ok with never seeing their families, homeworlds, and familiar places ever again. Make it a generation ship that essentially creates its own self-sustaining populace as it ventures further and further out. The command structure would probably have to be far more by committee, not just a captain and first officer. It would have to have several scout ships that are probably roughly NX 01 sized, and the Prime Directive would have to be seriously amended to ensure the safety and sustainability of the crew. I think at a certain point, pretty early, the Federation and Starfleet, would have to go out of contact. I think about that incredible scene in Interstellar where they come back after the 30 minutes/13 years on the wave planet and get the last video messages from Earth. Those are the stakes that would have to be on a show like this to make it compelling. Seeing how a diverse culture forms itself, not just operates within the form of Starfleet and Federation. I think it could be amazing, I just also think that anyone who made it and watched it would have to be really ok with it bearing little resemblance to what we classically think of as Trek. It could still be full of innovation, optimism, and societal commentary, but it would need to radically change the way it goes about framing those stories.