Even the uneducated tend to be better off in a country with a high education average than in a country where everybody is on their level. I'd rather be an illiterate in the Sweden, Switzerland or the USA (to take a few samples from all over the spectrum between welfare and market) than in any of the many countries that never succeeded in building a true culture of education.
You may question the causality of this (does education cause wealth or does wealth cause education?) but i doubt that it would even be possible to bootstrap high education with a market-only approach even under the most beneficial circumstances otherwise. I'm no expert in the history of American education institutions, but i'd be surprised if they were not founded with intentions more along the lines of the greater good of the colony or whatever local scope the founders were thinking of, than along the lines of offering even better opportunities for the rich. At the time, most of the truly rich were probably quite happy sending their offspring back to England anyway.