But oddly enough not PE teachers, who tend to be the highest paid public employees in the state -- https://247wallst.com/special-report/2020/09/21/these-are-th...
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).
Football coaches bring in literal millions in revenue, your Alabama example costs 8MM/year in salary but returns around 150MM in sponsorship/ad revenue/donations/etc.
https://www.businessinsider.com/schools-most-revenue-college...
And people wonder why there's a STEM crisis. When your society had decided it's more important to employ multiple full time extra curricular activity coaches for a high school while cutting STEM investment (and thus outsourcing the function) you're on the fast track to the bottom of the pile.