The taxpayer funding is for Harvard's research activities, not for its undergraduate teaching. The undergraduate teaching is funded by tuition (often paid in full by international students) and by returns on the endowment (including some earmarked for financial aid).

> they could vastly grow their class size without lowering standards

The issue isn't the quality of the students they are accepting, but the resources to educate and house them, including classroom space, dorms, and staff.