Here's the sad part, at least in my experience over the last decade with this online fandom. They can't do random nobodies. Star Trek is very self-referential and that is baked in to its DNA, as certain as phasers and transporters. This is a part of fiction that often times annoys me, but the evidence is painfully clear at this point that if they did a ship of nobody's they would need a hook. Prodigy has Janeway, Lower Decks is constantly referring to Trek's past. Burnham was connected to Sarek, Picard is self-explanatory.They should have did a ship we never heard of before starting on a "normal" 5 year mission.
Maybe after Strange New Worlds is done we will get something new. But, I would be surprised.