From everything I've read/seen/heard

• Jay Hill wants to be a head coach
• Jay Hill loves Utah (the state) and wants to stay here
• Jay Hill loves Utah (the program/university) and would rather be there than anywhere else

Obviously he's a professional and is doing a great job at BYU (despite his history with Utah).

It's fairly rare for someone to ascend from DC to HC, unless the HC retires or his hired away while the team is doing well (yes, I know, Bronco). If you're doing well enough at the coordinator spot to be in the running for HC, the HC normally won't be fired.  BYU/Bronco was a bit of an exception due to 1) limited HC options and 2) off-field factors being part of the reason BYU moved on from Crowton.

So if Hill stays at BYU...he has a path to become BYU HC (if Kalani gets fired since Kalani isn't going anywhere) or the Utah HC (if Scalley gets fired). If he goes to Utah, it becomes very difficult to become the Utah HC (if Scalley fails, he probably takes Hill down with him) but sets up a good path to become the BYU HC.

The best path to Utah HC (or HC in general) then is by staying at BYU. I was just considering the immediate implications - he's got more history with Utah and would likely rather be there in a vacuum...but I do think you're right that his goal to be HC is bigger than his desire to be at Utah