At many of the top schools (Ivies, Duke, Stanford, etc.), there are around 30,000 applicants or more. As a result, the admissions rate (especially in RD) is below 10%.
Obviously this prediction can’t be entirely accurate, but… how many of those 30,000 applicants would you say have, RELATIVE to other applicants, little to no realistic chance at admission (with things like: low test scores at 25% level or below, few extracurriculars and/or no leadership, no legacy/URM status/hooks, etc.)??
IMO each of the schools can fill up many times over with qualified applicants who would be capable of succeeding at the institution.
@happy1 I definitely agree with that. I was just wondering what people think about what the number of students closer to the “unqualified” end would be (disregarding those who get in with the help of sports, legacy, URM status, etc.).
Unqualified? 20% at most, and no, I have no basis for that number, nor does anyone here. 
Tufts posted an article saying their reps recommended 40% of students for admission. Tufts is a little easier to get into than some of the schools you are thinking of (14% acceptance rate) but I’d imagine they have a similar number. So to answer your question, 60%, give or take in either direction.
Note that this is different from only being academically qualified (which was around 80% for Tufts).
Source: http://admissions.tufts.edu/blogs/inside-admissions/post/decision-time/
Probably 80%+ are qualified to enter the school and have a reasonable chance of graduating. As for reasonable chance at admissions? I’d guess more than half are culled after the first read. The numbers are that tremendous.