This is one of those things that gets tricky because of the number of factors involved. I've watched this debate at my alma mater for a decade or so and its boiled down to this:

As state funding decreased, lottery scholarship funding increased almost in parallel.

As lottery scholarships increased, tuition increased.

Administrative costs skyrocketed.

Lastly and most importantly though, when people in high school take out student loans they have no concept of what debt repayment looks like or feels like. They have no idea what taxes coming out of your paycheck looks like in terms of cash flow. They have no concept of housing costs in that cash flow. Job loss or gaining employment is not factored in and what THAT does to cash flow and debt payments.

When students graduate all they know is that they got into school X and they need to pay for it.

The one true check on prices going up despite ALL other factors is the number of people who will say "not for that price" which thanks to student loans is virtually nonexistent because even if you say that somebody else will just slide into your spot.

Pure supply and demand. If cost is not a check on demand, cost will increase.