I think many Americans imagine the above to be infeasible and that university is somehow inherently expensive.

However, university can be very cheap. Here in Sweden university education, which is here funded in the way proposed above (i.e. the government pays for it all, for those students who get in) costs the state less than high school education costs the state (72 000 SEK/a for university, 124 300 SEK/a for high school).

I imagine that it could be the same way in the US.