Just a theory. I'd be interested in opinions, especially from any poor people who are parents. I'll note that this applies mostly to poor white parents specifically (lots of poor black mothers are plenty strict).
Everyone wants their kids to be cool. The idea that other kids at school might be just a little bit jealous of our kids makes us feel good. This is just a reality of human vanity.
If you are middle or upper class, you usually scratch this itch so to speak by buying stuff for your kid. If they have cool clothes and the latest tech gadgets, the other kids will envy them.
Poor people can't really compete by trying to outspend other parents, but they can give their kids something their classmates will envy: freedom. Sure, the rich third grader might have the most expensive iPhone X, but that kid is going to be jealous of the poor kid when he finds out that the poor kid gets to eat all the junk food he wants and stay up until midnight watching trashy TV. Once the kids get to high school, you can substitute alcohol for junk food and staying out all night partying for staying up until midnight watching TV.
Basically the idea -- conscious or subconscious -- is to parent in a way that other kids will think is cool rather than to parent in a way that sets your kid up for a good life.