If it results in worse behavior, then framing it as "encouraging improvements" is misleading. And if it's about encouraging improvements, then it should encourage the improvement from (3) to (2), rather than condemn it for being not (1), thereby actually encouraging (4).
Nobody "proved" anything. Proof is for math and alcohol, as they say.
I wouldn't have thought of it as begging the question, because it didn't occur to me that the empirical question of what the results are was in dispute! Yes, I suppose if you believe that this sort of Copenhagen-based complaining actually consistently leads people to do (1) rather than (2), rather than mostly resulting in (4), there would be little reason to have a problem with it. As it is, I'm not prepared to argue that empirical question right now, so I'm just going to note that I disagree and and that there's any number of examples of (4) out there.
