I actually think it would be the shrewdest move they could make, but let me qualify it: I think Hayward is a really good player. I think a lot of his value doesn't show up in the boxscore like AK. And for a lot of reasons, I would have no problem if they signed him to a reasonable extension this summer (even though I personally would wait till he's an RFA.)
But from an asset management perspective, I think his perceived value is higher than his actual value. Conversely, Burks perceived value is lower. Favors is the only guy getting an extension, and the only question is how much.
IF the Jazz are convinced he's going to be either the A or B star of the future, then you don't deal him except in a megadeal. But IF they see him as a quality third or fourth piece on a good team, THEN you explore what assets he can bring back BECAUSE you're already thinking about how you're going to lock in Favors, Kanter, and Burks/Bledsoe as the pillars.
For me, I like a future four of Favors/Kanter/Bledsoe/Burks much more than with Hayward in Burks' place.