As a result, the poor and even middle class have to jump over one real barrier, their lack of funds, and more importantly, like the Elephant that learns young that he cannot break the chains and never tries again, over their own state of mind, their own prison set by the terms of those who trying to help taught them to avoid anything but doing the same that keeps them poor.
While this might be true in your early years, if you live in a country where university is free, you are in a much better position. There are countries with an excellent educational system that is not based on money. You can get a very good Bachelor degree without spending much money. For the post grad education you might need to spend some more money, but at this point it should be possible to get financial support. And the rich kids can't do much about it if you study hard you will succeed. Good connections can help you get a position after university, but it comes down to your skills to keep that job and climb up the corporate ladder.
This is a perfect sample of the middle class mentality of a developed country. Get free education, college, climb up the ladder = work for someone else. Nothing really wrong with it, but that will only elevate the status of one in a million.
RE "rich kids cannot do much about it" - so naïve, so beautiful ... and so wrong. They will create their own exclusive schools, the will mingle with their "equals" their dads own the company of that corporate ladder you want to climb and they will be placed high on it before you can even start. If you have talent, do something for yourself.