I don't recall him ever saying that he had "head coach aspirations". I mean, what coach ultimately wouldn't want to be running their own program? But still, I don't remember him ever expressing that to any Utah media at least.
What I do recall him saying is that he's looking to stay in one place for awhile and that he loves his job, the people he works with, and that his family is happy. I think as some have stated that giving him the DC job was just a way of not giving him a reason to go elsewhere. He wouldn't have gotten a HC job for a few more years anyway so why does he need to go elsewhere when he's happy here?
No, I think we'll see him in Provo for a little while longer yet. The coaching profession at this level is so fluid anyway that you won't see many guys stay in the same position/town long anyway. But I would hazard to guess that Jaime will be here for at least another 3-4 years until his daughters get a little older. By that point he will have established one of the best defenses in the country year in and year out and other schools will be practically knocking down his door to offer him boatloads of money and titles to get him to leave Provo.
I actually don't think we'll see a coaching change for at least another few years. In my opinion, the most likely candidates besides Hill are Anae and Reynolds and with both having sons in the program I don't see them leaving for awhile. Doman may be offered another QB coach job but I doubt he'd leave Provo for another. Not only does he have some of the best recruits in the country to work with the next half decade years but I think he's a BYU guy through and through ad is totally loyal to Bronco.