So there's ample evidence that all Trek series don't have to follow the same formula of being centered on a ship and its command crew. It's been done numerous times in tie-in literature, so there's no reason it couldn't be done on TV.
Just because something can work in tie-lin literature doesn't mean it can work for TV, though. They're fundamentally different animals with different goals and markets in mind.
Tie-in literature presumes you already care about the setting, and about specific characters. It's perfectly reasonable to expect that you might be interested in an entire novel about the Cardassian Elim Garak, or from the perspective of a Klingon starship.
That's a harder sell with a Star Trek TV series, as any Trek TV series will want to bring in an audience unfamiliar to the franchise, even as it utilizes familiar elements.
So yeah, you're going to want human anchors for whatever the setting of the series is, and more often than not you'll want them to be Starfleet.