Not that I have any expertise but here are my criteria for the prefect coach (not happening).
In no particular order
Must be able to assemble and manage a great set of coaches. See Urban for a great team at first.
Must have or be able to create good relationships with the various Florida high school coaches and some outside of Florida for recruiting purposes. The coaching team is a big part of this.
Must be aware of communication with the media, fans, etc. Mullen was a total idiot here. Aware means doing this correctly not just thinking.
Must support academics and personal growth of his players. Few if any coaches have done this as well as I would expect especially the personals growth factors.
Must be able to play the politics required, internally, externally, and with boosters.
Must have an absolute commitment to obeying the various rules, and his personal conduct. This might exclude some who have bad issues in their past, but perhaps they have learned.
Now getting all this is impossible.
I think we will see someone who is not even well known by this group, because many that we talk about are not coming here.
Now our AD needs to go for his lack of supervision especially in the woman's basketball program. A good AD would be in direct communication with the players and supervise (directly or indirectly) his employees.
My last straw with Mullen was two things in his last game. Not even trying to win in regulation, and not taking an time out in overtime before the two point conversion. I don't understand how anybody can care that little about their job and not resign, but that is just me.
Comment as you desire, they will be interesting.