Exactly. And what public policy needs to do is revoke the non-profit status of schools that fail to make any effort to expand despite having an abundance of resources and qualified candidates.
Harvard could easily accommodate 20,000 undergrads given the size and quality of its applicant pool. That fact that it doesn't spend a penny of its $30 billion endowment doing so reveals that its mission is brand management, not education. And that's perfectly fine. But it shouldn't enjoy a tax-advantaged status predicated on the make-believe that its a philanthropic organization.