They need to improve the position. Exum and Burke aren't good enough today and as you noted Burke hurts the team because he takes so many poor shots and is so inefficient and not a good distributor.

I am not sure what the solution is however, because as you stated Burke has such low trade value and Exum needs minutes to develop and there aren't a lot of good options in the backup veteran pg market.

I guess they could ride it out through this season and then make a move at the trade deadline or next off-season, although if that's the course I think it's unlikely the jazz are a playoff team.

I have some serious concerns about Exum and whether or not he can ever be more than a serviceable offense of player? He has speed but shows little ability or desire to get into the paint or near the rim at this point of his career. Most elite point guards will show elite offense skills in spurts during their rookie season and I didn't see any of that from Exum. I guess there were games he made a few good passes or hit some outside shots; hopefully he can at least improve on shooting since most teams sag off and dare him to shoot since he doesn't currently shoot a good percentage.