One of those many things that, for quite some time, I had been wondering about in the sense that I had stored it in the folder "phenomena not understood by me", but not in the sense that I had taken steps to transfer it into the "phenomena understood by me" folder is that Germany has so few private schools, compared to the U.K. and the U.S. Now there seems to be an obvious hypothesis. That is, Germany has a tiered (tracked) school system, while the U.K. and the U.S. do not. Hence, in order to separate your kids from the riff-raff, you don't need to send them to a private school if you're in Germany (provided they manage to get into a first-tier school).
That obviously entails the hypothesis that untracked school systems bring about private schools. If you compare countries, you'll want to adjust for the right variables. Someone else do it!