Possibly. But that's not the main point either. Comparing profit & not-for-profit universities would be an interesting study, however.
I've got degrees from both. I see good & bad with both forms, no black & white, no clear cut dividing lines.
Some of the "for-profits" make me sick with their corrupt marketing. Some colleges make me sick with tenured profs who are coasting to retirement embarrassing the whole profession. But, those are the extremes, granted.
The Major point is that when a group of folks who want a service or product are given subsidies whether from the Gov. or other sources, the price of those goods & services tend to rise reducing the value of the subsidies.
FWIW, I'm 3 mi from the fastest growing non-profit college in Ohio: Stark State, next door to a branch of Kent State. (full disclosure, my health insurance agency is one of two that serve their students. However sales have been about 5% of original projections.) Construction goes on year-round. They can't meet the demand. Either tuition rises or folks go to lesser schools or both. Now, these are broad trends that can years to emerge, thus there can be lots of anomalies.
The main point is that whenever the Gov intervenes in the economy there is a domino effect not unlike the "Trickle Down" or "Trickle Up" theories.
Its not a question of gov. student aid or none either. Its recognizing the long-term effects that reduce the benefits of those targeted by the Federal program. Then, using the analysis to design more effective programs. According to Darwin, its adapt to survive or die.