Personally, I don’t know what would happen.
Obviously the sorts of things they say might happen are more nuanced than that. I think a fair summary is they tend to argue that on the scale of generations, the rate of new gifting will go down materially without legacy admissions. This would at least eventually force down their sustainable spending track, which in turn would ultimately reduce their ability to provide an extremely competitive, and highly subsidized, education to as many students.
That sort of argument is not as simple as saying “all” their new gifts “will stop”. And accordingly, it is harder to dismiss its plausibility. But whether that outcome is actually likely, that I don’t know.
So again the things they tend to argue are more nuanced than this. One of the things they argue, for example, is that very large gifts ultimately play an outsized role in their long-term financial plans. It is again not necessary for their arguments that a “majority” of donors “stop” giving. It might be sufficient, for example, if “some” very large donors “gave less”.
Now part of that comes up in the context of donors lists, which is actually a separate form of preferential admissions. But such donors lists are inherently backward looking. What they are arguing in the legacy context is basically that multi-generational family relationships are forward looking. Such that even if, say, none of generation A or B were such large donors, if they hit it big with one of generation C, then it could all have been worth it financially.
Again, these are sufficiently complex arguments that it is hard to simply waive them away as implausible. But whether it is actually likely, I don’t know personally.