Where is the example of a functioning civilization without strong public education?

Uhhh. Detroit.
Without the private schools here kids would get no education.
The democratic process in the form of elected officials grinds away at the system.
Not a week goes by without scandal breaking concerning some sort of criminal activity by the school board, teachers union or other group.
Maybe you're from an area of the country that has not yet experienced the entropic backlash from the vibrancy a city like Detroit once had.
Wherever you have gained your "B.S." from, know that your community will soon be joining ours, it's just a matter of time.