You never try to meta-analyze them with perhaps a state or country moderator?

I misunderstood you again; for some reason I got it into my head that you were asking about getting a point estimate of a secondary correlation that enters (as a nuisance parameter) into a meta-analysis of some primary quantity.

Yeah, if I were interested in a population-level correlation in its own right I might of course try meta-analyzing it with moderators like state or country.