It’s because the “Modern” Public School System was set up by Horance Mann and John Dewey in the late 19th and Early/Mid 20th Century after they had looked at the “Education” System in Germany during Bismark. The German System and Prison were kinda similer. Oh Bismarkian Germany is where T. Roosevelt, W. Wilson and FDR got alot of their BAD “Progressive” Ideas from.
Bismarck had a conservative streak and some classical notions of good statesmanship to him—on both grounds, unlike the Roosevelts—but in salvaging the particularity of Prussia he attempted to impose it, top-down and in draconian fashion, upon all of Germany.
Thank you for mentioning these points. The history of anything is really that thing itself and tends to go a long way toward explaining why it is the way it is.