Its very unlikely he wont improve his efficiency. PGs almost always improve their efficiency their third NBA season. Also like you said we have a better bench where he wont be required to score as much. He has shown the ability to pass more and is able to facilitate when there are players around him that are capable scorers. He was asked to score and shoot a lot last season. There was a bunch of D-league talent around him coming off the bench, I think he did what he was asked to do, shoot a lot. He also played good defense at the end of last season. There is 0 reason to believe he wont continue to play good defense like he did the end of last season. If you see 0 NBA starting skills in him then we should try and buy him out and move on. Clearly the Jazz FO and coaching staff see more in him than you do and I think you greatly undervalue him.
Its funny how a player I didnt like when we drafted him, never wanted him and still dont want, I have to stick up for on this board since he is so hated and undervalued here. But this board needs a bad guy on their team. We have to hate 1 player to the point of going over the top.
Burke is probably not a starter but I think he will be a decent backup pg that is a score first, high energy, vocal bench leader, who plays decent defense and needs to be guarded closely since he can score in a variety of ways.