You really think we can educate short-sightedness out of people? Or laziness? I think you're kidding yourself.
But more: You think "the haves" are greedy. But the haves usually got the good education. It didn't fix the problem.
And, even if the majority of people are in fact not greedy (or power hungry), it only takes a minority of greedy, power-hungry people to ruin things. Take the USSR. Those who were power-hungry and ruthless wound up in power. They produced what such people produce, no matter what the ideology and the rhetoric said.
If you're going to create an ideal system, you have to keep those people from ruining it. And the answer isn't to create a system powerful enough to keep those people in check, because those people will be drawn to the power they can have by running the system. Soon enough, they'll be in power - if not this generation, then the next.
Utopians always bank on the perfectibility of human nature. The available evidence is strongly against that view of humanity. And no, fixing the education system and the criminal justice system won't do it. They will help, and we should by all means pursue both fixes. But they won't let us build a utopia.