Who pays the utility bills? Professor and administrative salaries? Is anyone allowed in just due to having a diploma? What keeps rampant cronyism and end of year cost splurges to keep high budget levels for the next year? Who sets the budget? How does enforcement work, government employees doing enforcing?
In short how do you pay for it given the already spiraling out of control costs of higher education?
Are you saying charging high tuition is responsible for making US universities better? Correlation alone does not equal causation. Is there any evidence for this statement?
I can't speak for Switzerland but all universities in England charge the same for UK students with nothing upfront. Sure they don't have space for everybody who meets the minimum but that's inevitable. There are no legacy admissions, athletic admissions, positive discrimination etc. Everybody goes through the same process.
In short how do you pay for it given the already spiraling out of control costs of higher education?