Public education is failing our children because our society is failing our children. Parents are ed up, schools are ed up, kids are ed up, and none of this exists in a vacuum.
It is all a product of how we, as a culture, value education. It's not about learning anymore; it's about succeeding. It's about progressing, about graduating, about ing leveling up. By and large, people will do just as much as they have to in order to move forward -- students put forth the minimum effort to get a passing grade, parents put forth the minimal effort to make sure their kids don't drop out, people do just enough at work to make sure they aren't fired, and teachers (some, not all) will do just enough to make sure that there isn't a riot in the classroom. Even in a college atmosphere, in upper division major specific classes, I find that truly engaging with the material tends to be the exception, and not the rule.
There needs to be a complete paradigm shift in order to remove the biases that this country has against taking a genuine interest in something. Caring too much -- about learning, about intellect, about people, whatever -- is to be ridiculed. At every level, and in every setting. Enthusiasm is silly. Commitment and dedication mean that you've sold out. Instead we reward indifference and dumb luck (and if the months of "real American" rhetoric we were all treated to isn't proof of this, I don't know what is).
Until this changes, wholly, and at every level, there's no hope of really improving our education system. Public or private.