As far as I can tell, that is a bug in the German system, not a feature.Also the whole general attitude is different to the States, it's not about being the best or working the hardest, it's about everyone having what they need and a little bit more and the social security system reflects that. People in general will always have enough to live because the government will support them financially. It's just a very different mindset.
No, but other things definitely do. I am sure that a young person coming out Gymnasium has class advantages over one coming out of Hauptschule, even if the government is providing much of the basic needs for most everyone. In any society where some people have more and some less, class differences exists.So maybe the big "class-difference" is that money doesn't define you as much as it does in the States.