I think my two cents would be (after seeing helpful posts here that were unfortunately deleted):
-full pay by itself is not a hook at an Ivy
-however, each of these schools absolutely wants and needs full pay students
-so they get their full pay students from other hooked applicants (legacies, athletes, etc.)
Harvard was the example given. If you believe athletes and legacies are full pay, you can build pretty quickly to the ~45% of their class that is full pay. So my opinion is that admissions departments (even Harvard’s) absolutely have a sense for what percentage of their class will be full pay and they aim for a certain minimum number one way or another. They do not like to dip into their endowment.