I think it is more complicated than that. Bourdieu (_Homo Academicus_) demonstrates that the class system is replicated by the divisions within the academe, graduates from certain departments but not other being "tracked" to influential positions. Consequently, high tuition may not necessarily serve as an entry barrier to higher classes - it might be simply a result of "academic keynesianism:" government payments to private institutions to maintain a certain level of demand for their products.
In "classical" transaction cost economics, third party payments (i.e. payments made on behalf someone else, e.g. gov't reimbursing colleges for each student enrolled) create "information asymmetry" that will lead to profiteering by profit-orineted vendors. In that theory, a not-for-profit status (which most private schools in this country have) is supposed to take away the profiteering incentive. But in real world, that is not what is happening. Universities increase tuition as much as "market" - subsidized by gov't third party payments, can bear it.
The solution to this problem is quite simple - elimination of student loans and similar mechanism that benefit private universities, and increased funding of public universities.
wojtek