The CDC has guidance for how colleges should handle students who test positive for Covid. You cannot have a student who has tested positive living in the dorms with other students.

You do not need to be in the hospital to be sick, no?

Colleges and schools in general are also very unforgiving of sick time, compared to work.

If you miss a week or two of a difficult class, you may not be able to make up for that lost time in order to pass. With some classes only being offered at specific quarters/semesters and many being impacted, a single failed or dropped class can put you a year behind graduation, assuming you can pay for it. If a professor or teaching assistants gets sick, it would have pretty significant impacts for a larger number of students.