I'd say the significantly improved literacy rates throughout the world are certainly helping the case for current education schemes (public and private, public merely gives access to more people than costly private education).

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).