>"how limited the value of a particular correlation generally proves to be"

I would go further. In my medical research work I saw dozens, probably hundreds of "statistically significant" correlations between different variables in a rather small dataset. I found them just by taking different subsets or summarizing the same data in a few different ways.

I didn't find any interesting and so published nothing about them, but I am sure others could build entire careers out of coming up with narratives to explain those correlations.

I have to think that people who have trouble finding correlations are either clueless about exploring the data (eg have only ever looked at dynamite plots of their results) or are measuring something so swamped by instrumental noise it is meaningless.