There are two broad solutions to these kinds of problems: demand-side and supply-side. This article is another data point in exactly why demand-side solutions are short term if they work at all. More likely they don't work.
A supply-side solution to education would be to create more spaces in quality higher education and to make those places cheap or free by government subsidy, often with price controls on the receiving institution. This is largely how most of the developed world works.
A demand-side solution is to make something more accessible, which has the net effect of increasing demand. This almost always raises prices. It's no surprise that money backed by the government has increased prices. It's inevitable. Demand for high-quality college places still exceeds supply so those colleges can (and do) respond by increasing costs. Sometimes that extra money benefits the students through better facilities (eg a new library, better and/or more dorms, etc). Often however it's lost in subsidizing college sports, which most colleges lose money on, and inflating administrative costs. Division 1 football coaches make millions a year for a supposedly amateur (that's what one of the As in NCAA stands for) competition. That extra money makes those programs more expensive to run too through the same means.
We see the same problem in housing. Nearly all legislative efforts are demand-side (eg programs to help first homebuyers) where what we need is simply to increase housing supply by building more units, making more current units available or both. But that runs afoul of vested interests where our homes have become retirement accounts.
It's worth noting that many elite colleges are sitting on eye-watering endowments that could easily be used to pay for tuition but they largely don't do that (outside of a few programs for students from poorer backgrounds).
Pretty much all of this is by design. Post-WW2 there was a concerted campaign to charge for things that were once cheap or free including health care and education. This is nothing more than economic bondage, the developed world's equivalent of Pakistani brick kilns. A person saddled with debt is a compliant worker who will show up to work and not complain or fight for better working conditions. That's literally the point.
It's why the prison population is used as cheap labor. It's why most states like illegal immigration. It's why states are enacting child labor laws. My point is that all of this, including spiralling student debt, is a systemic problem.
Education should be free.