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I agree on the publication record. But the school you go to has a huge effect on your ability to publish. This is well documented.

Go to top PhD program -> publish top journal easier -> attain tenure track job.

It all comes down to prestige in the end. This is aside from very hard sciences where true ground breaking results cannot be ignored.

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Even in things like applied math, it's pretty arbitrary which assumptions and formulations become standardized when tackling similar problems (and it usually comes down to the effects of prestige on your network/ 'reach': the more prominent people you get your ideas in front of, the more likely your work is to become the 'state of the art' default approach, and the more prestigious your university (and the professors you collaborate with), the easier it is to get your ideas in front of important people.

Theres a huge feedback loop that is very opaque

Most publications these days have many authors. Your first papers are published with your advisor and other collaborators, and that establishes your history of publishing on the topic in good journals. Also, peer reviewers don't know or care which school your degree came from.

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