This "approach" to research was debunked as pseudoscience long ago (eg here is one from 1967[1], and that wasn't the first)... So the answer is: no one knows what works or doesn't, (edit: at least not based on the usual claimed method of drawing conclusions from the data).
[1] http://www.fisme.science.uu.nl/staff/christianb/downloads/me...
Probably never will happen in social science, and in much of medicine. Too many confounding variables.
I'm willing to bet that if we threw away all the "knowledge" we obtained from p-tests, and stuck only to the methodology you espouse, we would know far less true stuff than we do currently (albeit we would not know a lot of false stuff).
Simply put: Even though there is a lot of noise, we do know more using these methods. And the nice thing about bad results due to misuse of statistics: Much of it is not reproducible.
Ultimately, the problem isn't the use of these statistical methods. The problem is the lack of emphasis on reproducibility.
This is some kind of talking point. I'm not sure who is behind it, but it is totally false. There are tons of examples of this, especially from the pre-NHST era:
https://en.wikipedia.org/wiki/Kleiber%27s_law
https://en.wikipedia.org/wiki/Law_of_mass_action
http://www.ncbi.nlm.nih.gov/pubmed/17845298
https://en.wikipedia.org/wiki/Law_of_effect
http://www.tandfonline.com/doi/pdf/10.1080/00221309.1934.991...
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2916857/
https://en.wikipedia.org/wiki/Compartmental_models_in_epidem...
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2007940/pdf/brjc...
Besides that–how is what you're proposing different from the status quo? Every social program ever was born from a theory, i. e. "education creates agency, and is therefore a better investment than direct money grants".
It just happens to be a lot more difficult to run randomised experiments in sociology, because it is (by definition) the study of very large, interconnected systems. Societies just don't lend themselves to the sort of reductionism that gave us all the advances in physics and mathematics.