Davis was not fired after going to the Sweet 16, in fact, he wasn't actually fired at all. It was known for most, if not all of his last season that his contract was not going to be renewed. The team played well in his last tourney and made it to the Sweet 16, as sort of a FU to Bowlsby.
As an aside, the bulk of the fans wanted Dr Tom gone too.
Also, I don't think Fran's seat is warm at all. It probably should be, but I don't think it is.
You can't fire Fran now. That should have been done two years ago. But after barely missing out on the Sweet 16 last year? Forget about it.