the institution should bear the cost That assumes they really feel it. If a school charges you $500,000 per year for tuition and then gives you financial aid

the institution should bear the cost That assumes they really feel it. If a school charges you $500,000 per year for tuition and then gives you financial aid of $480,000 per year, they aren't really giving you that money. If a school extends you $150,000 in credit, and then in 20 years you've only paid $40,000 of it back, they haven't really lost $110,000. They are just practicing perfect price discrimination, getting the most money from the people most willing to pay, backed up by the government who is doing the work of auditing people's tax records to ensure compliance.