Without getting into why one can not prove a negative, I totally agree with the spirit of your question: Where are the tests?
I think you are referring to a triple-blind study. In a double blind, all participants know they are in a test situation, all participants know they might receive the control option (drug, device, whatever), and all participants must give their consent in writing, usually multiple times. By the way, the control isn't automatically a placebo. Many tests try to resolve differences in performance, and the control is the old thing being compared to the new thing. In these tests, everyone is getting some level of treatment. My mom was in such a test.
In a triple-blind study, none of the subjects know that they are in a test situation, and some receive no treatment while thinking that they are getting the standard stuff. Ethical issues abound, but consider that only a triple-blind study has a chance of producing unbiased results. Expectations, positive or negative, color *everything*, and even the best double-blind studies have reliability issues.