The honest answer is because it brings in sponsorship money from local businesses who want to advertise to locals who are going to go to games, it brings in alumni money from any former student who made it big in athletics (and those who have fond memories of athletics), and it brings in money from people who think a particular team/coach is good and thus want to have their kids go there. Yes, school choice is a big enough thing that I know families who have moved so their kid is in a particular school’s district.

Image is a big part of that. It’s also because many well-meaning people see athletics as a way to help a student get out of being poor, offer financial mobility, etc. So athletics get pushed from many people coming from different angles.