I don't really understand this kind of categorical bashing of public education. Descartes, Aristotle, and most "others" you're thinking of lived in societies where the majority couldn't even read, and they didn't consider that a problem. Reading without moving your lips was considered an exceptional skill during the middle ages (or so I've heard).
Are you sure they really knew much more about a practical system of education than we do now?
> Reading without moving your lips was considered an exceptional skill during the middle ages (or so I've heard).
You are refering to what contemporaries wrote about Thomas Aquinas, a well-renowned theologist in medieval era. I believe he was considered a genius because he could read without moving your lips.
While it is a good food for thought for intellectual capabilities, one should also take note that in his time books were not what books as we know. No typography existed and whitespacing blocks between words were non-existent. Truly, they were mostly transcribed words with sometimes bad spelling and without a paragraph break. To read without reading out aloud meant that the reader had a mental capability to quickly parse out words, form a sentence, understand what the author meant out of context.
Are you sure they really knew much more about a practical system of education than we do now?