How would you establish Snoke wants him to kill Leia personally? You’d run into the issue of why his wingmen fired on the bridge if he was meant to do it, and also if that they can sense that Leia isn’t dead or not, because they probably would assume she was otherwise.

EDIT: Also, that if Snoke wants him to kill Leia personally, then later is content with all of the rebels, including Leia, die like sitting ducks in the transports. Maybe that killing Rey would suffice? But you’d still need to make that clear, and explain why his wingmen destroyed the bridge if that was Kylo’s task.