There is a difference between maximizing revenue and maximizing profits (which is what a for-profit entity would do).College athletics is absolutely a for-profit entity. Pretending otherwise is burying your head in the sand.
Firstly, the Media is definitely for-profit, and they are paying for everything.
And all that media money going to the ADs - that's not all going to educate kids, not even close. Maybe 25%? Lots of people (coaches are the biggest single benefactor) are making millions and millions. ADs and lots of associated meatpacking glitterati within the ADs are also getting paid a lot to do a little. Building over-the-top facilities. Private jet recruiting trips. All those expenses are not suggestive of non-profit behavior or mission. Just because they don't have "owners" and just because they are a 501c3 doesnt change that behavior.
The guy running United Way is not making $8M a year with a 5 year guaranteed contract buyout.
I’m not sure if your last sentence was sarcasm or not. But you should take a look at some non-profit CEO salaries

Nonprofit Compensation Packages of $1 Million or More
Which charities compensate their executives most highly. CharityWatch's salary information is calculated using the IRS Form 990.