It's not that they're pumping money in that's the problem, it's the place they decided to pump that causes the issue. Financial aid and guaranteed loans are on the side that increases many student's ability to pay. The alternative is to give money directly to schools (perhaps based on enrollment numbers to mimic the "market based" approach of tuition aid). This brings student's ability to pay back down and would force schools to lower, or at least freeze tuition,.
Private financial institutions would no longer loan nearly as much money to students to pay for college, so less money would go through the chain of (student after graduation)->lender->(student when they were in school)->school. This means that overall, less money would be moving from students/graduates to schools.
Schools would have to find a way to manage with smaller budgets or get more government support.
