It seems that Houston is tired of being a launching pad for coaches hoping to get a major Power 5 job.
Houston hired offensive coordinator Major Applewhite to be their head coach on Friday, with speculation being that Applewhite would supply continuity to the program better than a Lane Kiffin type of coach. Applewhite replaces the effective Tom Herman, and based on this comment from Houston president Renu Khator, they definitely don't care that Herman is gone at this point.
Related: Houston booster explains why Lane Kiffin wasn't hired
It sounds like Houston isn't happy.
Herman, Sumlin, and Briles are all former Houston head coaches that turned the job around for a bigger head coaching gig in Texas. However, Briles has since been fired from Baylor and many surmise that Sumlin is on the hot seat at Texas A&M.
Hoping that Herman does better is a nice gesture, but that definitely didn't seem like the point; it seems like Khator's point was that the greener pastures that previous Houston coaches left for didn't turn out to be too green after all.