Economy depends on productivity and innovation. Who would've thought that the people like Gates, Jobs, Zuckerberg and Ellison would create so much wealth and so many jobs without college degree. Robust US economy enabled them bringing their innovation to fruition but I'm afraid if they lived in another country they wouldn't be able to do that. Of course every country depends on higher education but sometimes creativity can outperform formal education.
I think public vs private is irrelevant because if you are productive as a worker or innovative as a entrepreneur result is the only thing that counts.