Do they really make money? Maybe they do! That's 7 schools out of how many state schools supporting teams. Anyway, there are differing views as to profitability.
https://www.bestcolleges.com/news/analysis/2020/11/20/do-college-sports-make-money/
The above article presents a case that there is a lot of "creative accounting “ going on to show profitability. I've seen other similar articles.
For state schools is the taxpayer paying for an education institution or a sports entertainment institution? It's becoming increasingly harder to do both and maintain a semblance of honesty and educational standards. Maybe honesty and educational standards are not important?
From the article you posted:
“only a handful of schools actually make money through college athletics.”
That handful of athletic programs are the only ones that should exist.