You’re right that endowment is the biggest driver of whether private schools offer need blind admissions AND whether they meet full need of admitted students.
Wake is need aware in admissions but does meet full need of those admitted. The fact that the meet full need of admitted students is probably a driving factor behind the policy being discussed by OP.
By contrast, some private schools are need-blind in admissions but don’t meet full demonstrated need of admitted students (including my child’s college, Villanova).
If a school is need aware in admission or need blind but doesn’t meet full needs…it kind of de facto becomes a “rich kid” school.
The most elite private schools typically have a large enough endowment (and priorities) to be need blind in admissions AND meet full need.
The schools with the highest endowments, including several ivies, are need blind, define need generously, and meet full need…sometimes without loans.
I wish all schools could do that but it does take a LOT of money to do it.