I don't think it's fair to blame a school system for failing to educate the children of a single mother on welfare as well as those with PHD's from Harvard. And I am not suggesting that it's genetic. If you took identical twins and adopted one into each of those family's I would expect to see a similar performance gap.

The US has some 'great' public schools, and some 'terrible' ones. But, the difference has a lot more to do with the students than people are comfortable admitting. The private / public gap in education is also a lot less than you might expect.