Your mistake is thinking that school produced those scientists. They produced themselves despite school, not because of it, and they thrived because Germany invested heavily higher education and research. Science in Germany was due to German philosophy, higher education, and lots of funds.
Universities in 1900 are indistinguishable from what we have now. In 1900 they were still targeted at the wealthy and unusually talented. Now they are just extended sunday school. Obedience training for adults.
