All the characters should come and go, that's what makes it realistic for the military. The lead character shouldn't be magically immune from being transferred or killed. I like the idea of a big cast of characters in which many characters are important but any could be killed without warning and without following the expected rules of TV, a la Game of Thrones
Alterntatively, you could have a show that follows one character through all their transfers, regardless of what ship they are assigned to. It would be the most interesting if this character was someone other than an obvious lead character type like a ship's captain. How about someone without particular power within the Starfleet command structure - an outsider like Quark, a Romulan spy, a Harry Mudd type rogue who keeps having run-ins with Starfleet?