You're absolutely wrong. Even for residents at the well-off University of Texas in the well-off state of Texas pay $5,000 per semester for tuition only (tons of fees added to this). That's $40,000 for four years. In Germany you'd be hard pressed to find tuition higher than 500 euros per semester.

And don't get me started on graduate and professional degrees. In Europe you study medicine, law, dentistry etc as an undergraduate in a 5-6 year program. In the US you need to do an undergraduate degree for four-years plus four more years of graduate school to become a physician. The cost of the graduate degree itself is anywhere from $150,000-$300,000.

Tuition in Norway is $80 USD/semester, as one data point. Are state funded US universities cheaper than this?

(You also pay a couple of cents if you want to print documents, but these are the only fees I have paid in six years of University).

Tuition in Europe varies a lot. In some countries it may cost €2000 per year, in others it's free.