So, here's the crazy thing. Back-of-the-envelope, but it gives a picture. Harvard has 20,000 students, give or take. Plucking a number from the air, let's say that one year of study is $50,000. Across 20,000 students, that's $1B in tuition fees. Harvard's endownment is $36B.
For less than 3% of their endowment, they could give 'free education'. Obviously the whole picture is a little more complex, but it does add some context around funding.