A rich kid is much more likely to leave an impact on the world and this is what these schools want. I once (10 years ago?) read an article about exactly this. The comparison were some US elite high school that strictly select on IQ and alumni were much less successful than expected (yet, more happy in live). George W went to Yale as far as I remember. I doubt that he scored super high in any IQ test. But he was undoubtedly very successful in live.
"Ivies really wanted to promote social justice, they would let in more poor kids"
This is not their main priority.
As a side note: The Economist MBA rankings 2021 have raised eyebrows because European schools rankings increased so much: https://whichmba.economist.com/ranking/full-time-mba