The problem is that many US universities are private. So when the government puts money into loans and grants for students, the universities just raise tuition, rather than expanding to accept more students. In the end it's just a transfer from the public to university administrators. To really expand access to education we'd have to have many more public universities.
And anyway, the problem with education isn't that it's not available to enough people. Smart, motivated kids can get a university education even if they're poor. We have enough academics and highly-educated workers for our economic needs. The problem is that it's become a class marker. Many, many people don't want more degrees out there, because it would make their own degree less valuable. Others are desperate to get a degree at any cost, not because it improves their career prospects, but because it confers high status. So taking on huge debt for a useless degree is fine, and in fact good, because it's conspicuous consumption. Of course, debt sucks, so once they have the degree, loan forgiveness is very much in their interest, but not publicly-funded university.
On the larger question, I think it's a cultural thing. America was settled by people leaving stifling societies to go it alone: Europe at first, then the American establishment on the east coast. The frontier is gone, but that value system persists, and self-reliance and independence are hugely important to many people in the US. There's a pretty good argument to be made that American democracy arose because the wilderness was right there and if they didn't get a say in government, people would just move beyond its reach. That culture is has served us well, but we've run out of frontier, and we're starting to feel the social pressures that Europe has had for millennia. There's no escape from the state, so the way to get ahead is to work the system, get a larger share of the pie rather than growing it, and so on. The pushback to that is to demand more fairness from the system, ie, a welfare state.