It is not hard to do, the data just isn't public and such data will never become public. Therefore public researchers will always lag behind private ones, since the private ones have access to the interesting data.
Edit: Also it is not a theory, I have seen internal studies on this myself.
Here is the thing: this discussion is not about scores or about candidate performance. It's about the question whether the same candidate would be better assessed with a technical interview over a non-technical interview. Since you are not even addressing the question at hand I call it bullshit.
Also, something which has no written proof of and there is no consensus about among at least a group of respectable people and/or institutions is just a theory.
And the third one, you somehow assume that public sector is somehow an inferior player to the market who might not even have relevant data. That's again a theory though and not necessarily correct, here are a few examples of publicly funded software engineer employers: CERN, NASA and the US Army.
I don't understand the problem here, all technical interviews are also non-technical interviews since they are still communicating with a human and not just doing problems on a computer. If we didn't care about the human interaction part we'd just put them in a room alone with a set of problems.
Also I think you don't understand how much recruiters hate this process, they'd do anything to remove it since they have no way to game technical interviews. So they work hard to change the interview process at Google to something more soft like we have in other areas, but the evidence points to soft interviews being worse.
And you might not believe me, but I definitely believe me and the people deciding how to hire people at these companies certainly believe in the studies they do, so there is no way they will change the process. These interviews are here to stay, and until we have some new methods nobody has tried yet it won't change. You can complain all you want, but the best companies will be using this process as they scale up since nothing else works at the moment. Some other things might work for small companies, but as soon as the founder can't interview everyone himself it breaks.
OP is just saying we can't prove it doesn't work.