under Rose, 1 under Stew, and 4 diff coaches at UNLV (only a few for Tark).
https://en.m.wikipedia.org/wiki/Dave_Rice_(basketball)
So Rose had the most time with him, and you could argue the Jimmer era is what led to Rice's attractiveness as a head coach.
I don't see him getting that gig directly out of USU, given how they plateaued.
Overall get your points about strengths, limitations, and they are best men for the job.