Bingo. Also the problem with meta-analysis of certain kinds of studies (say, observational ones) is the file-drawer effect: people don't report negative result

Bingo. Also the problem with meta-analysis of certain kinds of studies (say, observational ones) is the file-drawer effect: people don't report negative results. So you can go from a bunch of studies that show an effect (usually small) at marginal statistical significance to a meta-analysis that shows very high statistical significance when there is really no effect there. I don't think we have to worry about the file-drawer effect much with controversial COVID treatments, though. Do you?