First of all, I don't believe that's actually true based on what I've seen: what seems to be more often the case is that the tickets pay for the marketing and some of the athletic infrastructure.

Meanwhile, the coaches are being paid millions of dollars per year. I don't care how much money the athletic program is bringing in; that's not a responsible use of the money. (I get that it's something of a prisoner's dilemma at the individual institution level; I'm more talking about the broader issue.) If you have the money to pay the coaches $2M/year, that means you could, instead, stop paying your adjunct professors and regular staff sub-poverty wages, and/or perform proper maintenance on the buildings.

And do not get me started on the economics of stadium construction.

They're profitable because they pay their workers (the athletes) next-to-nothing. And even so, colleges would be better off spinning off their teams into professional entities that pay royalties to use the school's name. At the very least, it's one less distraction for the college administration and they can focus on their actual jobs: education and research.