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The randomized control trial is a great example where a superintelligence actually could do better by using a non-random strategy. Ideally, an AI could take its whole prior into account and do a value of information calculation. Even if it had no useful prior, that would just mean that any method of choosing is equally "random" under the the AI's knowledge.
Bayesian adaptive clinical trial designs place subjects in treatment groups based on a posterior distribution. (Clinical trials accrue patients gradually, so you don't have to assign the patients using the prior: you assign new patients using the posterior conditioned on observations of the current patients.)
These adaptive trials are, as you conjecture, much more efficient than traditional randomized trials.
Example: I-SPY 2. Assigns patients to treatments based on their "biomarkers" (biological measurements made on the patients) and the posterior derived from previous patients.
When I heard one of the authors explain adaptive trials in a talk, he said they were based on multi-armed bandit theory, with a utility function that combines accuracy of results with welfare of the patients in the trial.
However, unlike in conventional multi-armed bandit theory, the trial design still makes random decisions! The trials are still sort of randomized: "adaptively randomized," with patients having a higher chance of being assigned to certain groups than others, based on the current posterior distribution.