Good point. Kids of poorer school districts still have the prestigious admissions system stacked against them, in many ways, but simply knowing that Ivy/MIT/Stanford/etc. may be options will lead some to look into it, and some will then have information, time, and means to make their application look plausible.
As a young teen, I applied for financial aid, to a state school, and got a nonviable response, since my parents of 6 kids could afford to contribute zero, but some bureaucracy thought otherwise.
So I went to Community College part time, while working at a store, and then was a co-op student, and worked my way up from there. After working in industry, I went to grad school, at an Ivy and MIT, and only then did I learn what successful undergrad applications tend to look like, and also that there's various financial assistance available (including some not advertised).
My story is not of the system working. I've seen so much systemic class nonsense and rigging (and sometimes bad behavior by people who feel entitled to whatever they can grab). Being at a disadvantage in those games doesn't stop once you're nominally in. But the relatively recent need-blind admissions, and family income thresholds for tuition, help a lot, especially if we can pair that with getting the information/advising about successful applications to everyone.