US schools get far less from the state than Europe and Asia. You can find many school budgets online, including sources of revenue. So this is easy to check. [2] lets you look at country per capita spending on tertiary education - the regions you mention tend to spend significantly more tax dollars than the US does.
The result is that most European and Asian schools get funded by taxpayers, i.e., those not attending university end up helping pay for those who do, while in the US more of the funding is paid by people that attend schools.
Also, the US, as a result, also ends up with a higher percentage of adults with college degrees than those with state sponsored schools [1], since those places tend to make it harder to go to college, since taxpayer pressure on cost reduces opportunity.
[1] https://en.wikipedia.org/wiki/List_of_countries_by_tertiary_...
