Even assuming that there is some small enough set of great schools to use them for that signaling as Google traditionally did -- I do not think that's a rationa

Even assuming that there is some small enough set of great schools to use them for that signaling as Google traditionally did -- I do not think that's a rational assumption, but that's another discussion -- then at least in the USA you should also know the candidate's parents' financial situation and whether their parents went to the same elite schools. For starters, because it's a lot easier to "get in" if you have no trouble paying for it, and you have your "legacy admissions." If you really think XYZ is that great, you should really want to hire the people who fought to get in, fought to succeed, and did.