I agree that universities are not going to tighten the purse strings unless they have no choice. The cause, as you mention, is the feds throwing money at the education system. Therefore, the only logical solution is to remove that. You say you don't want to limit access to education, but the world isn't perfect. If you want everyone to have access (meaning having access to funding via loans) then you must accept the consequences of that. I, personally, don't have an issue with limiting access. Education that involves universities with buildings, faculty, land to maintain, etc. are not infinite resources. The natural check on the usage of resources is cost. Presumably, you don't sit around letting your sink run all day because you would wind up with a massive water bill. If people want to go to college and get an education, there is a cost involved. There are always going to be those who are unable to pay due to extreme financial situations. But that's why there are scholarship programs, grants, etc. that exist.
The education system used to work fairly well in this country several decades ago. You used to be able to go to college and pay for it in a very reasonable amount of time even through minimum wage jobs. Loans weren't even necessary. And when the end user pays the bills, the connection to cost is there so people pay attention to what it really costs because they bare the brunt of it right away and it's not hidden (so to speak) from them through loans that are paid off over 10-20 years.
It was only when the government decided that something was "wrong" and needed to be improved that the system started going to shit and getting ever more expensive and the product (education) getting worse and worse - the quality of the education people are paying for nowadays is abysmal half the time.
I discussed this recently in another thread with some specific numbers attached to my explanation:
https://news.ycombinator.com/item?id=15647956