How big of an advantage do you have if you can pay full tuition?

@prospect1: Use of the term"endowment preservation," in the context you employed, seems to indicate that you may not entirely understand how endowments operate – and with rather strict contractual and managerial strictures. An endowment normally is a contract between the donor(s) and the university. Use of an endowment’s funds is rigidly limited by this contract. In addition, the university’s leadership generally allows only a small percentage (perhaps 5 percent, on average, annually) of endowments to be expended in any year (and only for the purpose delineated in the contact), thereby ensuring the perpetual nature of endowments.

Therefore, for example, even if every leader at university X agreed that it would be wise to withdraw major capital from their aggregate $7.5B endowment to increase massively need-based scholarship, they could not do so because a great deal (probably, a lot more than half) of their endowed capital was donated for other purposes (e. g., professorships, athletic scholarships, maintenance of certain facilities, library enhancements, and much more). More specifically, financial aid officials consequentially have a defined amount (endowment withdrawals plus annual giving) that can be awarded in any year for grants and scholarship. They could not exceed this limit, even if they wanted to.
Accordingly, the “erosion” you suggest really is unlikely, if not impossible.

Obviously, a serious financial market downturn can – and will – adversely effect an endowment’s value. However, market upturns restore and increase endowments. To illustrate, endowments at many of the most-selective institutions have already more-than-regained all of the losses suffered in the market decline of seven years ago.