Are you really going to label Head Coaches of major sports programs as PE teachers?

The reason they are paid highly is because they carry the majority of responsibility in the success of sports teams, which generate revenue (in the hundreds of millions in the case of Football and Basketball) for the athletic departments of these universities. That revenue is used to fund literally every other collegiate sport, and provide scholarships to tens of thousands of students nationally. These positions are unique because they are simultaneously extremely competitive (most coaches are fired within 5 years) and tied (loosely) to a public entity.

To call them PE teachers is a ridiculous presumption, no matter how overpaid you believe they are (and rightly so).