At first I was confused about how this would work, but thinking a little about it, it should be fairly easy. Give some researchers (randomly selected!) results from studies that are not RCTs ("control") and others RCT-based results ("treatment") to replicate. See which group manages to replicate more results.

Expensive, yes. Would I like to see it? Heck yes, if nothing else as a way to trick the establishment into doing more replication studies.

If the meta-RCT shows that RCTs are efficacious, then RCT's are effective. But, if the meta-RCT shows that RCTs are not efficacious, that means the meta-RCT, which is also an RCT, cannot be trusted, which means that RCTs are still effective.

> Is there any RCT done on evaluating the efficacy of RCT?

What is the set of possible results from the experiment you propose? What function are you going to test: randomness in general, some special RCT event, maybe some doctor who loves to break some double blind experiments?

A good post on the subject: https://slatestarcodex.com/2014/04/28/the-control-group-is-o...

Reminds me of: https://m.xkcd.com/1526/