No matter what big guys you've got on the team, you need to be able to get them the ball and Burke is the best point guard in the draft.
Randy Foye and Gordon Hayward shot the ball well but just didn't get enough looks. Adding a distributor will do a lot for the Jazz shooters and help young Alec Burks as well. Last year, Mo Williams and Jamal Tinsley were the primary point guards, so there is certainly room for improvement from a distribution standpoint.
While this pick may help them become a more balanced team, the real urgent need here is to figure out what to do with Jefferson and Milsap. Are they going to shell out the dough these guys want and probably can get somewhere else or let them go. The most likely scenario is that only one stays a Utah resident, but I'm not going to try to anticipate which one it'll be.
Tyrone Corbin had this team knocking on the door of the NBA playoffs with a young team. I don't anticipate them to make a big leap next year, but if Burke is able to contribute and they are able to retain a good part of their front court production, they will continue to make incremental improvements.