Paying via taxes is not charging students.
You do not pay taxes based on your use of public education or use of any other public service but based on your income and/or wealth.
If you do not make sufficient income as a student to pay taxes or enough taxes to cover the cost of your education your public education is in fact free to you.
Why do you think OP is not aware that there are costs to be paid but merely disagrees with using sports as a way to pay for it?
You even used the word Utopian. Well most universities are not financed via sports even non public ones. Far from Utopian.