https://nces.ed.gov/NAAL/lit_history.asp
We had poor literacy, we introduced public education, literacy improved.
One major advantage of public education is breaking a particular cycle that would occur without it for many people. If you're uneducated or undereducated you are not in a position to educate your own children. You need a school or a tutor to help. Without that, your children are likely going to end up similarly undereducated.
Public schools are a democratizing factor that can significantly reduce inequality in education, and consequently inequality in life outcomes (as measured by financial and other success).
http://www.huffingtonpost.com/2013/09/06/illiteracy-rate_n_3...
>Public schools are a democratizing factor
That's true, everyone get's an equally poor education.
Even in a situation where the world requires a new solution to education, the burden of proof in terms of a particular solution's efficacy lies not with the old approach but the new.
That is to say, public education needs to demonstrate how it is objectively better suited than historic methods of education.