That’s an interesting point that looking at student preferences, as measured by which school cross admits choose, would product a somewhat different rank ordering.
A majority will choose either Harvard or Yale over Princeton, as noted Stanford is winning a higher percentage in recent years, a good number of students from Notre Dame families will go there regardless of where else they get in, etc.
That’s not to say a revealed preference ranking is necessarily a better approach, but it would lead to somewhat different results.