Isn’t this already a solved problem with models that are used in various countries in the EU? Where the education is financed through taxes, thus you don’t pay anything up front, but keep paying for it for the rest of your life.
The problem of college affordability is arguably another dimension of the housing crisis. You can look at the numbers yourself. Yet oddly I've never seen this pointed out or discussed, not in the media or anywhere else.
In principle an easy way to lower the cost of college would be for public universities to invest in building more subsidized or free dormitories. The problem is that most of the popular coastal universities are in areas where development is absurdly expensive and contentious, even for government.
It’s not perfect but it’s a good starting point.