Yes, being born where you're born, and in the family, community and culture you're born into is pure luck. So is being born into a wealthy family or a poor one. But you have to be competent to earn wealth and you have to be competent to keep it. If you're incompetent and born poor you probably won't build much of anything. If you're incompetent and rich you'll probably squander it. I'm not saying that anyone can overcome anything with sheer competence, but most people have the opportunities around them to build a life they'd be happy with if they use those opportunities wisely.
I'd say education is like any service, you get what you pay for. And I'd add to that, the public education system in the US is a grift and our poor aren't getting what we pay for. But I'll also point out that there was a time when you got no education at all unless you could afford it, or unless you were very driven to teach yourself.@aral