Good school? Bad school? Schools here are what you make of them. You screw off, you go to a bad school.
So, you think that a public school in the inner-cities is going to get as much funding from their property taxes as a public school in rich suburbs? Initiative certainly plays a large role, trying to deny it would be stupid, but there is such a thing as opportunity too. For one, a reputable college would much rather have students from more reputable high schools.

You go to a little town high school (hundreds of them in Kansas), and no, you won't get the same advanced placement oppotunities I had, but when you go to a University (and state universities are NOT prohibitvely expensive, especially with the vast amounts of aid available to poorer families [like me for example].
Sorry, big companies would rather have someone from Harvard than from a State University. Harvard is more expensive than your state universities.

If you don't want to pay with your first born child, don't go to a private university), then everything will even out.
How many of the lawyers in the top firms of New York do you think aren't from a major law school? Now, don't blow-up I'm not saying you have to go to the big private schools to succeed, that would be ludicrous, I'm saying that you would tend to do much better if you went to one of them.

What is wrong with using contacts?
Nothing.

I refuse to believe that there some monolithic entity in the USA that keeps any person or group of people poor. You want something? Earn it.
I never said there was, and I agree with you. You are arguing against the strawman that I illustrated before. It isn't a simple idea, socio-economic mobility, there are many factors. Your success is not soley dependant on the effort you put in, like it or not.