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You'll need to be a lot more specific if you want a specific answer.
It's whomever is doing the trial.
They will surely go with strong prior. However, it's already like this even with frequentist methods (it just takes a different form): math cannot force honesty out of anyone. The advantage of the Bayesian approach is that priors are explicit, and others can judge them more easily.
The basic idea of how the FDA process works is that it's extremely predefined and doesn't allow the person who wants the approval to cherry pick statistics.
It seems like your approach is to provide more flexibility. Did I get the wrong impression?