Thing is, I'm not convinced that it makes sense even as the show has set it up. When early on it appeared to be doing Andromeda, with the Federation having fallen, it made sense that Discovery's crew would stay together on their ship because they didn't have many other options. But once they introduced this massive multi vessel Starfleet headquarters, with a functioning chain of command and strategic ops they should have been quickly absorbed and reassigned, mostly to duplicating the spore drive. At that point, keeping a 900 year out of date ship and crew together operationally was a quite odd decision and only makes sense out of universe, to keep the story going.