It's not that they suck at statistics. It's that their statistics and experimental designs are artificially stuck in the dark ages. This is forced on the world by the academic publishing industry - you publish this way, or you perish. The completely unsurprising result is a reproducibility crisis that undermines the entire field. Check out "Bernoulli's Fallacy" for a good overview.

My theory isn't that Psychologists are bad at statistics. It's that the remaining problems involve lots of messy interactions and messy data that all but require statistical techniques. We just don't have the tools to extract obvious causality amidst such complexity.

Not really - it just shows up so much in psychology because they need statistics much more than, say, physics. Most physics programs in the US do not even teach statistics as a subject.

medicine, biomedical, economics, cancer biology have similar issues hence the reproducibility crisis in those fields