Meta-analysis is a mirror of empirical estimates, really, in my opinion. It doesn't solve the underlying problems of research integrity or lack thereof, but doesn't create them either. It
does allow you to model what is being reported though, to be explicit about your assumptions of estimates being reported in the field and how to go about aggregating them.
I agree about open data, for what it's worth, and even things like preregistration to some extent. There's a lot about dishonest research that has nothing to do with the statistics you use, or maybe even your design. It's sort of a never-ending arms race in that regard, and just as important to address the incentive structures that drive it in the first place.
