This was exactly the kind of meta study I had in mind. The statistics would be complex, but I'm not sure they would be impossible to a sufficiently skilled and resourced researcher, you'd just have to have someone who fully understood how to go beyond the basics of looking for trends based on two or three variables and how to correctly control for and weight multiple covariants.
One could identify measures of validity such as replicability (which after all is already pretty much established as a benchmark of scientific merit) or numbers of citations (easily possible given the sort of search functions available in most academic libraries these days) and look for significant differences between individual countries and aggregated political groupings, significant differences between academic disciplines, correlations based on population size and various metrics of socioeconomic success, national crime rates, availability and nature of research grants, whether they are publicly or privately funded, etc.
I'm actually mildly curious if anything along these lines already exists in the literature and I'm not at all sure it is out of the question.
It would be a huge undertaking but one might imagine a wealth of possible hypotheses becoming testable, from broad questions such as looking for significant differences between political systems (such as whether we see significant differences in the rates of fraudulent publishing between privately and publicly funded research and does that relationship hold between broadly capitalist and socialist systems) to more specific and detailing modelling of optimal conditions for both pure and applied research.