My issue is the flippant and silly claim that "[i]t's possible to imagine a version of academia where results that can be attributed to noise don't get published".
Take a sampling of a large number of papers, give them some sort of rating based on whether they provide enough information to reproduce, how clear their experimental and analytical methodology was, whether their primary data and scripts are available, etc, and then look at that rating versus their citations.
Hopefully, better papers get more attention and more citations.
(And yeah, "peer review" as it is done before a paper is published is not supposed to establish a paper as correct, it is supposed to validate it as interesting. Poor peer review ultimately makes a journal uninteresting, which means it might as well not exist.)
Well, with a single paper the odds indeed are that it's noise. That's why we need reproduction. Now of course a paper needs to be published for it to be replicated later. But the paper (and/or supplemental material) should contain all possible things the research team can think of that are relevant to reproducing it - otherwise it's setting itself up to be unverifiable in practice. Papers that are unverifiable in practice should not be publishable at all, because a) they won't be reproduced and thus it'll be forever indistinguishable from noise, and b) there's no way to determine whether it's real research, or a cleverly crafted bullshit.