I've suggested and advocated that before and more than a few have said that it "wouldn't be Star Trek"
Face it, you can suggest nearly anything around here and someone will say it's not Star Trek
"Immunity" for lead characters is a characteristic of TV, not any particular series, but it's breaking down on cable. It's just one of those broadcast traditions that wouldn't necessarily continue with Star Trek
on cable or streaming, along with the episodic structure and PG-13 approach.
American Horror Story
has an interesting approach: have each season be a different story, an anthology-by-season format. They also rehire a lot of the same actors to play different characters, which Star Trek
also has a fine tradition of doing. One season, an actor is playing a human, next season they're a Vulcan or Cardassian, etc.
seems to be using this strategy to hang onto hot actors like Zachary Quinto who have movie careers or are in demand for TV, and don't want to commit to several seasons of a TV series. But with a mere 13 episode season, it's likely they can fit a TV series in, if they have the option of skipping a season when it's not feasible.