Extreme skepticism of social science findings is warranted for some subfields, but when it comes to intelligence, humanity has actually learned a lot.
I guess I could imagine a study, something like: look at kids of professors, in particular identical twins vs fraternal. Not all children will be National Merit Finalists, but among those that are, do you find identical twin pairs more often? Even that is subject to environmental effects, though, because potentially identical twins are raised differently!
In my opinion, Human nature is too complicate to poke at many of these factors, and talking about genetics quickly devolves into racism and elitism.
Some of these are interventions that we’ve already found to prevent wasting of ability (as you cite in another comment); others might be nutritional or environmental changes we could make to better support development in utero or as children develop.
Giving everyone 5% “better brains” would be a huge win for the world, but the sociological factors you mention preclude widespread scientific study.
Perhaps studies of early adopted children would another pathway for study, but there seems to be little appetite for IQ study in general.