Saying something like "choose to live in a nice neighborhood" is analogous to saying "if you're poor you won't be given access to good schooling" because poor people can't choose to live in a nice neighborhood, no matter how hard they are willing to work. Not to mention poor children. And you're presenting a false dichotomy here. We don't have to choose between rewarding people who work hard and providing good education to everyone. We are absolutely capable of doing both, we just choose not to because the system in place has clear benefits to the people who are creating/perpetuating that system. Much like the caste system in India. I'm absolutely, in very clear terms, not proposing we implement the Indian education system. That should be obvious.
What you're defining as American is very dangerous. You're saying quite literally "to be American is to have the individual right succeed no matter the expense to others". While that's a very Hacker New mentality, and quite obviously how America operates, I wouldn't call it particularly equal or meritocratic. If hard work was rewarded, the hard working lower class Americans who have three jobs would be given access to these neighborhoods and school-systems. But this is transparently not the case.
You seem to be someone who believes you should seek the rewards of your hard work, and I agree with you 100%. However, what you're missing is that the rewards system in the US is not designed to reward those who are putting in the most effort. Nor is it designed to reward the children who are driven and likely to be successful. The rewards and incentives in the US currently favor anyone who already has money, no matter what they are actually providing to society. And it certainly provides no opportunities to promising young children who happen to be from lower-class backgrounds... but at this point I'm just stating facts.