Are you saying that TNG, DS9, and Voyager shouldn't have been called Star Trek? I have no objection to them having done that, because they were continuing the story started in TOS, or exploring other parts of the universe that was essentially a future part of TOS. And when TOS charcters (McCoy, Scotty, Sarek, Spock, and Sulu) guested on these shows, they weren't "reimagined" into some modern version that would appeal to a younger generation and that would be unpalatable to many TOS viewers.
I'm just trying to understand your point. You're saying that a Star Trek series based on Gene Roddenberry's Star Trek featuring Star Trek characters Kirk and Spock on the Starship Enterprise shouldn't be called Star Trek, but a series all but ignoring the source material featuring all new character should be called Star Trek. That seems exactly backwards.
I've been wondering lately when the obsession with continuity happened. I don't remember anyone caring that much about continuity except in a broad sense even back during the early days of TNG. Brannon Braga wrote a lot of garbage, but his term "continuity porn" is entirely apt.