What she could not offer, of course, was a spot in a Power 5 conference. And in truth, that is the real reason Herman left: The name-brand teams in the Big 12, Atlantic Coast, Pacific-12, Big Ten and Southeastern Conferences regularly get to compete to be in the lucrative four-team College Football Playoff, which they essentially control. They get the best slots on television. They have unmatched fan and alumni support. It is easier for them to recruit the best high school players. They can absorb multimillion-dollar buyouts for hot coaches like Herman without breaking a sweat — while paying millions more to departing coaches whose contracts still have years to run. In football, especially, the Power 5 conferences are the insiders, their hands firmly on the controls, and everyone else is on the outside looking in.

This raises a painful question that Houston must now grapple with: For all of Khator’s ambition, and the team’s recent success, can Houston ever truly be a football power if it is not in a Power 5 conference? And will its head coaches always view it as a steppingstone rather than a destination?

It is not as if Khator has not tried to get into a major conference. This year, when the Big 12 was flirting with the idea of adding two members, four universities from the American Athletic Conference — Cincinnati, Memphis, Connecticut and Houston — vied to be considered. To anyone watching from the outside, it seemed as if Houston would be a shoo-in. (In the end, the conference decided to stay with its current 10 teams, in large part because its television partners objected to the expansion.)

After all, Houston is in the country’s eighth-largest media market, larger than any other Big 12 market. It is also a market that tends to prefer SEC games to Big 12 games, something Houston’s inclusion would probably have changed. Unlike the other three A.A.C. colleges, which were primarily basketball schools, Houston had shown that it knew how to build winning football teams and generate fan enthusiasm, even without the advantage of being in a Power 5 conference. The Big 12 already has four teams from Texas — Baylor, Texas, Texas Christian and Texas Tech — so Houston made geographic sense and had the potential to lead to heated rivalries.