He is currently under a head coach that is on a short leash. Maybe that means he could move into the HC job if Smith gets fired, but I don't think the prospect of him getting the job changes much if he goes to BYU. If anything it can make him more attractive that he had exposure to other coaches to learn from. Especially if that coach pitentially has an NBA pedigree. And there is only downside to his current situation. Being attached to a failed staff could be something an AD doesn't want to touch. Why promote a guy that was part of the reason things didn't work in the first place? This way Burgess gets out from under that and provides himself a little job security. And job security where he doesn't have to uproot his family is probably really nice.
The Utah bball fan support is terrible right now. Little fans in attendance and curtains. That can't be much fun. Also, it has to make his job so much harder. Harder to get NIL money. Harder to get kids to want to come. Why wouldnt you go somewhere that makes your job more fun?
The other thing is probably more personal but when Burgess first when up there his daughters were also at Utah. I am sure that was great to be close to them. They're not there anymore and that takes the family aspect out of the equation. In fact, I am pretty sure Burgess is in Utah County so BYU actually makes things like getting home easier on him.