Here we have
Bafög, but the situation becomes more and more similar.
No it doesn't really. Even after the introduction of study fees in some federal states in Germany, studying in Germany remains dirt cheap compared to the US (see JDR's debt reference). Studying in the US can easily
cost tens of thousands of $ if you go to a decent college/uni.
The linked document from the German Academic Foreign Agency quotes $12K - 16K annual fees on average for the US, ranging from $2K per year for a community college to $33K per year for a graduate study course at a university.
Our German €0.5K fees per semester completely pale in comparison.
The US educational system is also very achievement-based in my personal experience. You do not necessarily have to be rich to afford a good college/uni. The alternative is to be smart and work hard (starting in High School naturally). Then you might end up scoring a scholarship worth thousands of $ for a decent education.
It's still a bit unfair, of course, since the dumb, rich, lazy kids just need the dinero and you as a poor kid need to work your ass off to get on the same level but it is not entirely true that only rich kids can get a decent education. They are in a better position for sure but the possibility of a high ranking scholarship is open to everyone.
If you are poor but talented and very active in High School, getting excellent grades and partaking in lots of activities from the Speech & Debate Club to Economics to Sports etc. you have a pretty good chance to get a scholarship for a decent college.