Could the NCAA change this power structure? You bet it could. It could require that coaches be paid no more than, say, the highest paid professor at the university. (Suppress your gasps, please. I know it sounds un-American.) Wouldn’t that lead the best college coaches to go pro? Yes, it probably would — and that would be a good thing. In the corporate world of the National Football League and the National Basketball Association, the coach is just one important employee in the organization — and not the most important or the highest paid.

The consequence is that few professional coaches are surrounded by the cult of personality that we know so well from college sports. (Quick, how many current NFL coaches can you name other than your home team’s?) Those professional coaches who do have a cult either profess a philosophy of Zen minimalism, a la Phil Jackson, late of the Los Angeles Lakers, or are so fanatically competitive that they are hated and loved in equal parts, like Bill Belichick of the New England Patriots.

Make no mistake about it: The cult of the coach is the problem. It is heartwarming that, in the United States, the title “coach” has some of the same honorific qualities as “pastor,” “doctor” or “president.” But the most famous and prominent college coaches cannot be expected to behave responsibly when their institutional power is essentially absolute. When the university president is an unknown compared with his or her coach, is paid far less and doesn’t enjoy the same charismatic authority in the eyes of the alumni, there is no realistic way for the president to supervise that coach or his (and it is almost always his) program. The corruption of the incorruptible Paterno is a story of the absence of any structural check on his authority.

So why doesn’t the NCAA change this? Because the coach’s cult is good for business. College athletes play for a maximum of four years, and the best football and basketball players generally don’t stay that long. This is barely enough time to get them nationally known.

Rivalries between colleges can be branded, of course — but as any marketer knows, personalities sell better than abstract brands. The coaches are a crucial part of the product. That is a part of why the coaches make the big bucks. And in America, a high salary is a part of celebrity. This vicious cycle should end. There are, of course, some cult coaches with sterling reputations. But remember: Until year ago, Paterno was one of them.

Noah Feldman, a law professor at Harvard University and the author of “Scorpions: The Battles and Triumphs of FDR’s Great Supreme Court Justices,” is a Bloomberg View columnist.