Works in Germany as well (with a very low fee, nearly free).
We believe that education is a basic human right. The human rights are equal for all humans (listen, Usamericans: humans, not just "citizens"), therefore it must not happen that low income can hinder it. And that's also the reason why German universities regularly accept a good number of students from all over the world.
Why it "works"? Well it's simply the government's job to make it work. We, the people pay them for doing their job. As you might know, or not, in a democracy the people are the highest authority.
Yes, we actually don't know the numbers that are common over there, but I have heard that students get in debt for a huge part of their lifetime - which we consider a scandal and a shame for a country.