I agree with your concerns and in point of fact we used to do things a bit differently in this country; we used to expect corporations to PAY TAXES and thereby do their part to help fund public education from kindergarten on through a public university education. Shifting the burden of tuition costs from public funding onto students has accounted for a large percentage of that shocking increase in tuition you referred to.
Much of the rest of it can be accounted for by 'bloat', where university officials- almost never actually teaching faculty, mind you- excuse and explain increases that end up paying for fancy buildings (like football stadiums on campus, a controversial issue in my hometown right now) and ridiculous salaries for administrators and others who DON'T TEACH STUDENTS.
Only a small if still significant portion of that tuition increase can be put down to inflation.
For those who may blather on about how the average taxpayer shouldn't have to foot the bill for students attending public universities, I have lots and lots of very good reasons why this system helped make America great- and why trashing it is now contributing to our decline.
Worse, what we've gained in return for this terrible trade-off is tax cuts for the wealthy- a group that can certainly afford to pay their fair share AND would benefit greatly from a better educated populace.