Those schools aren't necessarily shittier...they are filled with kids that don't want to learn (and their parents increasingly blame the teachers for their failure).
Interesting hill to die on, but you do you.
But that's a little too nuanced for your straw man.
At the same school, several of her students have received large scholarships, including full four year rides to university. This is rare, of course, but does correlate very clearly with parents being involved in their children's education, encouraging them, and not having an anti-achievement peer group.
Middle class kids (and above) get good education handed to them on a silver platter while poor kids will have to fight tooth and nail to scrape their own education together.
It's not impossible but if you were that determined you could learn even better in a good school so the relative downside for poverty still persists. What you are setting yourself up for is not becoming poor. That's good but it is clearly not fair.