this is overstating the case. Throwing out all publications is ridiculous. Yes, many fail to replicate, but not nearly all. A larger concern may be that many fail to generalize (e.g. mouse cancer cures fail to work in humans).
It's true that it's hard to ignore all of the citations a reviewer suggests, but that's part of the role of an editor, and the response to reviewers (while being a frustrating exercise) can make it clear what is and isn't an appropriate citation, which serves as communication to the editor. Yes, this process is frustratingly low bandwidth