To be fair, if Ash is one of the Klingon pariahs, Mudd selling the ship to an enemy group of Klingon's wouldn't be part of "the plan."
This might make sense if you think of the Captain's chair as a bluetooth device. It has all these buttons and controls, but the captain's voice is the the only part with any authority. So, you reprogram what all the buttons on the chair do and the way commands go back and forth, the "chair" is non-critical but if you believe the chair is working correctly, you can get messed up.
Maybe all history of the Bee Gees is lost and they think Wyclef invented the song.
Mary Sue is a little bit of an outdated concept as it came from a ST fanfic no one read. So, I use the example of Poochie. Everyone knew who Poochie was and talked about him in every scene, but he didn't do all that much. So far, Burnham has been the key to every important part of the Klingon War and is in almost every scene. In fact, Stamets had much less screen time than Burnham, and didn't really appear in any scenes without her.
Tilly doesn't really make sense as a character as some of her traits are contradictory.