1. Colleges set exorbitantly high prices.
2. The government-supported system assesses families' ability to pay though FAFSA process, where you submit your tax returns (not that you have to, IRS is government as well) with your wage/business income, then list all your assets (minus retirement accounts such as 401Ks) and liabilities. Then the FAFSA spits out your expected contribution, TELLING you how much you can afford to pay for your kids education.
3. Colleges and government then use this number to determine how much "financial need" you have. They can "meet your financial need" by letting you pay less than the sticker price (it's called "need-based scholarship"), or allow to take loans on favorable terms to close the difference between the sticker price and your ability to pay (that they determined). More often it's a combination of the two (depending how desirable college is and how good of the student they perceive your kid to be).
Consider the quantity of people coming from outside the USA to study. It may be that foreigners looking for prestigious schools are searching in the USA because their own system is middling (except maybe for a flagship school?). Thus, they're also doing the damage to the USA's education market while not affecting their own domestic one.
Other countries typically regulate prices, preventing things from becoming expensive to begin with.
This applies to education, health care, housing, and more.
This is why Ivy League schools have endowments larger than the GDP of some micronations and are financially being run like hedge funds, while still simultaneously being supported with US taxpayer money. The progressive orthodoxy does not hold these institutions accountable for institutional greed and selfishness because of a shared cultural affinity between progressive politics and higher education, and because all of the negative externalities of the spiritual sins of selfishness and greed at institutional scale are forgiven for the virtue of being a nonprofit under the idiosyncratic, dogmatic priesthood of progressivism.
The US doesn't have progressives. We have conservatives and conservatives LARPing as progressives when it's financially convenient for them.
On a related note, this is also why Canada and the UK can make single-payer healthcare work and why the US can't. Some of those shadowy GOP dark money donors are the same faces that the public would associate with progressive thought leadership. They're following a Machiavellian playbook where they attempt to portray themselves as publicly virtuous while remaining the same soulless, greedy multimillionaires or billionaires that instinctively think from a place of unadulterated self interest behind the scenes.
The price signal is almost the other way around (the more expensive, the less likely it is to be a good place).