I think you are confusing schools like Harvard with your run of the mill state university. The latter rarely has much of an endowment to fund itself with.
My run of the mill state school has an endowment larger than than $500 million and still sent out emails begging alumni to donate to a fund to make sure students didn't go hungry in the early days of covid.
"A typical endowment consists of hundreds, sometimes thousands, of individual
funds. In most cases, the donors who have created these funds have set restrictions on how their donations may be spent. In 2007-8, about 78 percent of endowment assets at public institutions were under such restrictions; an average of 55 percent of the resources contained in private university endowments were restricted (See National Association of College and University Business Officers (NACUBO) 2008 Endowment Study). In such cases, money restricted for research in a specific subject, for example, may not be applied toward student financial aid, and vice versa. Donations are typically restricted to fund student scholarships, conduct specific kinds of research, finance specific programs to enhance undergraduate and graduate education, create professorships in specified fields, develop or maintain teaching and research facilities, or improve a wide range of campus activities, including the arts, public service, student housing, and athletics."
However, other articles go on to note that money is fungible, making the restrictions less onerous than they appear. If, for example, a specific restricted endowment fund is restricted to providing scholarships, it still reduces the amount of scholarship money the university has to provide out of general funds by the amount the restricted endowment provides, freeing up that money to be used elsewhere.
Profit. It's always profit. Higher education is nearly mandatory to get a good position and good salary. It's nearly a gateway. 30% of the population has a university degree in first world countries.
Forcing multiple thousands of dollars is a toll for a bridge where few alternatives exist. And in a country that considers so many things a business, this is of course run like a business ergo profit is very important.