I forgot about the pension obligations. Even if the boosters pay the salary, the school is on the hook long term if it is a defined benefit plan. I’m guessing coaches take the defined contribution 403b option since they would probably not be around long enough to vest in the plan. That is kind of the reason TIAA/CREF exists for college professors.
Since someone brought up concussions:
I got run over hard by former NFL player Ronnie Harmon in high school. I had him lined up for a tackle and bounced
off him like I wasn’t even there. He was a full grown man 5-11, 200lb of solid muscle with near olympic class speed
playing against boys. I’m bigger than him, but never stood a chance.
I love pro football but there is no way my kids were going to play in high school.
https://www.pro-football-reference.com/players/H/HarmRo00.htm