There are many public schools with Olympic sized swimming pools, and funding that would rival the better private schools any day of the week. Money and funding are not the problem... In Detroit, teachers get paid much more than the national average. And we know how well that school system does.
The problem is that for the last 40 years in the US, to bridge the gap between student groups to 1 standard deviation: the only thing that has worked was the systematic dumbing-down of teaching content and testing material (for example: with the elimination of written answers by multiple-choice questions, and 30-40 point curves on each test). Everything else failed. No matter how much money was thrown at the problem, no matter how many teachers were fired and replaced, no matter how many experts and better management staff were brought in from other parts of the nation, it just got worse.
So now we have one of the worst public education systems in America, all because no one could go into a class-room and ask the students that wanted to learn to raise their hand. And then present more challenging material to that group (relative to the other groups).
And I'm not talking about what we already have now - a few Advanced Placement classes, I'm talking about the entire education system being free to cater differently to A) students that want to learn and compete, B) students that need simpler material, and C) students that want to clown around.
Instead, we have a system that caters to the lowest-common-denominator (C) in the room at the expense of every other student. So no one get's taught anything that enhances the mind or prepares him/her for the challenges ahead.