I would like to look at FA from a different angle.
Please let me know if you personally have come across this point: Which schools have certain # of seats allocated to FA and which schools rather distribute the $ amount amongst the applicants that they love to see at school?
All schools have an FA budget. Does is matter how they decide to allocate it? Will this change your decision process? Regardless, other than some anecdotes, I doubt you’re going to find definitive answers to your question.
It might only matters in certain threshold of family income. Some schools prefer to offer a large amount of FA to limited number of applicants, vs some schools are more lenient on family income, lets say, if a family can contribute 75%-90% of tuition, but will have hardship for the last few $$$, they will not be dismissed.
At the end of the day, if a school accepts an applicant with insufficient FA (and the family cannot/will not come up with the difference) vs rejecting an applicant because the school can’t provide the FA, then the result is the same - the kid is not going to that school. I’m not aware of any school that is “lenient” with FA. Some schools, but not all, may contact the family before M10 and ask if they are able to send their kid with no (or limited) FA as @ChoatieMom can attest to. But I’m sure that’s a case-by-case basis and not part of a strategic plan.
Note that the admissions office and financial aid office at most of these schools operate under the same management (usually a Dean). If I were a Dean, and had a fixed financial aid budget, I would most certainly try to spread the $$ to as many students as possible.
But I imagine that every once in a while, a student catches everyone’s attention that they absolutely must have on campus. In these cases, I’m some of the wealthier schools would be willing to offer more FA. This again depends on each school, the institutional priorities and the FA budget.
Schools that are committed to SES diversity get it by having kids across the full spectrum - from full aid to none and everything in between.
How it is distributed in practice is anyone 's guess.