Universities with large endowments still charge tuition. The available proceeds from appreciation of the trust may not be enough to cover their operating expenses.
Universities aren't exactly a great model of freedom from private interests. And it's not clear why many of them do still charge tuition—i just assumed it was some effort to emphasize classism in a world where they also want to look gracious for paying for poor people.
And believe me, for the colleges I examined this at, tuition was a rounding error compared to the return on the endowment. It is just for aesthetics of charging students in a uniquely american show of stupidity.