That isn't to say aspects of it cannot be perpetuated within a new form. It can and the new could take different forms.
I think now it isn't advantageous nor truly desirable to remain tied to previous continuities. Whether it be Prime Universe or Abramsverse we should let it be and go forward. Learn and understand the best elements of the most successful Treks---TOS and TNG---and adapt them to the new form.
One thing I think is absolutely essential to return to is a core element of the best Star Trek: an adult approach. This doesn't mean gratuitous and graphic sex and violence, but rather a mature approach in tone. This also doesn't mean excluding the young at heart because the visual spectacle and sense of adventure can draw the youthful viewer just as it did for many of us when we were younger. But by working on multiple levels the show can appeal to varying age groups.
Another element I think matters is a return to ideas and issues periodically explored amidst the adventure. This was yet another core element that set Star Trek apart from the competition. It doesn't have to be heavy-handed (although occasionally it can be), but it does re-affirm the notion that popular entertainment can still have something to say and provoke thought and discussion.
If we forego those two core elements then whatever we're doing is no different than what everyone else is doing. And if that is the chosen approach then you might as well not bother doing Star Trek.
For myself I would prefer quality over quantity. To that end I would plan for something fitting a 10-13 episode season. I might go with each season having some sort of arc or plot threads running through it, but there needn't be a huge arc running throughout the series. Indeed I think this approach would make the show more accessible.
That could be done again with something that actually is Star Trek.
I agree with your post. What I would add is that if it works on multiple levels, as most Trek did, as you grow older, you remain a fan.
An example: I used to be obsessed with
Teenage Mutant Ninja Turtles. Loved it. Had all the Playmates figurines, turned in every Saturday to watch it. I would talk about it with my friends. I was 5-9 years old.
Now, I tune in to see what they did, but they hit their demographic sweet spot after the first TMNT movie (in 1989). It is more intelligent than it used to be, but it remains a children's cartoon.
It repeats this way with My Little Pony, Saved by the Bell, all those comedies from the 80s and 90s (Charles in Charge, Happy Days, Who's the Boss? Head of the Class, Friends, Victoria's Closet, Seinfeld), etc. Discarded them all. Discarded Saturday Night Live. Discarded The Tonight Show, Discarded Bill Maher's shows.
Star Trek, for different reasons throughout my life, has stuck with me. I started watching about the time I got out of TMNT. I would buy the books and figurines, the VHS tapes, and watch the re-runs. I was just as obsessed as I was over TMNT. But out of nostalgia, I went back and watched a few episodes I didn't like when I was growing up. And I found that Star Trek carried, with me, something more to it than my other interests.
If fans grow up and don't discard you, and you continue to make new fans, then you remain popular.