> The real problem is that peer reviewers can’t possibly replicate the study, and so are forced to look for inconsistencies in the papers.

This is a misunderstanding of the role of peer review. The point is not to prove that a paper is correct, the point is to ensure a minimum level of quality. You are entirely right that most reviewers cannot hope to reproduce the results presented, and very often for very good reasons. If I write 3 proposals over the course of a year to get some beam line on a neutron source, it is completely unrealistic to expect a referee to have the same level of commitment.

I think this hints at a more profound problem, which is that a lot of studies are not replicated. This is where the robustness of a scientific result comes from: anybody can make the same observation and reach the same conclusions under the same conditions. This is the real test, not whether you convinced 3 or 5 referees.

The real value of an article is not in whether it was peer reviewed (though the absence of peer review is a red flag). Instead, it is in whether different people confirmed its main results over the years that follow publication.