With all due respect, I disagree with this broad generalization. When my youngest started school we were in dire times financially - yet he is the head of his class. He saw us working hard to better our condition, and knew he had to work hard also, it wasn't going to be handed to him.
He was also naturally intelligent, something anyone can be regardless of their socioeconomic status. Money doesn't make people smart and lack of it doesn't make people stupid. Academically, it depends on your school system. There are some well-off kids here and some kids from "poorer" families, they are all given the same attention and will do what they will with that opportunity.
I do understand a lot of districts in deeply impoverished areas are lower quality, but I think that is a societal problem we need to change. If we ever want to end poverty, we need to empower children in that situation to grow and better themselves. That doesn't happen when we decide on broad terms that poor people can't be intelligent. In fact, a lot of intelligent people, geniuses even, don't function well in social situations and for that reason they struggle with being able to be employed. If we demonize and demoralize whole sections of society, where is the incentive to step up?
I've lived that scenario, being treated like a crumb for being poor. I didn't choose to have a husband with a broken back and year-long recovery, job loss and everything else that came upon us. We were both highly intelligent individuals. Fortunately, those who knew us in our community did what they could to help us, including the teachers at my sons school who saw his potential and didn't care that he was on the free lunch program and didn't have brand name clothing.