Stuff like Benford's law or the central limit theorem are a trivial observations that anyone with some basic statistics knowledge could have called out. But that also means anyone who has some education in the field could easily falsify plots to avoid that, so you will not catch real physicists with those methods. The problems in the paper that was eventually retracted were only visible to experts who actually work on this very topic. Here they talk about some of the abnormalities: https://www.nature.com/articles/s41586-021-03595-z

Looking forward to giving the Nature paper a read. I appreciate your time and wisdom!