This is a very hard problem to solve for a university alone. In India, there is affirmative action AKA "reservation" and trust me that system has it's own perils. I still think meritocracy is the way to go while having systems developed by the govt. to help the under privileged kids meet that bar.
Why should a college even choose the highest academic performers? It's an educational institution, not a contest.
At the end of the day, what is a college optimizing for, and why?
Colleges could be selecting for students who the college can provide the most value to, or which students need that college the most, or which students show the most potential for post-college success by the college's metrics.
It will inherently be a contest as long as admission rates are below 100% and schools' reputations are non-uniform. If you shake up admission criteria to be more holistic and less weighted on academic performance, applicants will refocus their attention and compete to satisfy the new set of criteria (at least those within their control).
I definitely wouldn't argue that colleges are optimizing for greatest societal benefit, but it would take a lot to truly align their self-interest with a selection process that doesn't heavily consider academic performance (particularly for private universities).
To address your point, though, I'll assume your use of "admissible" is synonymous with "admitted" students. An increase in rates would require that the number of admitted students increase relative to the size of the applicant pool. If the applicant pool increases with the number of admitted students there isn't necessarily an increase in the rate of admission depending on the relative increase in the size of the applicant pool. If we instead define "admissible" as meeting criteria for admission but not necessarily being admitted, I wouldn't be surprised to see a corresponding increase in admission standards to maintain existing admission rates. Interested to see if anybody has evidence to support or refute this based on historical trends in admission criteria (GPA, SAT, etc.) vs. admission rates.
I think this is what they're doing, and it's really hard to do that for a 17 or 18 year old kid beyond grades, test scores, and extra-curriculars. What would you suggest?
That said, economic status and academic performance correlate closely. A college that's very selective will necessarily filter out a lot of lower-income kids purely because it's hard to do extra-curriculars if you need to work after school and/or if you can't afford them, it's hard to get good grades if you're worried about whether you get to eat this week, etc.
My point being that Brown can be both need blind and not have a lot of lower-income kids there.