This interpretation of the reproducibility crisis is not supported by this massive international study, at least according to the last paragraphs of the origina

This interpretation of the reproducibility crisis is not supported by this massive international study, at least according to the last paragraphs of the original article (which quote someone directly addressing your concern). The results they found were that the studies that could not be successfully reproduced generally failed across all tested cultures, while the ones that could be successfully reproduced generally worked across all tested cultures. So it seems that there are some results in statistical psychology that are robust, but that researchers have not been sufficiently reliable at identifying which results those are.