Well, at the Ivies+, about 60% of the students are from the top 20% by income, and only about 5% are from the bottom 20% by income. So I guess that they aren’t really interested in poor kids who only have potential. I would guess that most of those 5% are kids who got into magnet schools, have at least as many achievements as the most accomplished of the rich kids, and have managed to secure a scholarship so that they can pay the $20,000 or so a year in residential costs, etc, that Ivies still require from even the poorest students.
What Ivies REALLY prefer are:
3. Legacies who have relatively high stats (top 15% in GPA and SAT/ACT, moderate ECs, no awards)
4. Athletes who have relatively high stats (top 15% in GPA and SAT/ACT, moderate ECs, athletic awards)
I would guess that there about twice as many of each of these as there are poor kids with high stats and amazing accomplishments. I would be surprised if there were more than a handful of poor students with potential in any given Ivy+.