I'm familiar with general statistics, but I'm no expert in Bayesian statistics. So perhaps I'm mistaken in what I'm about to say.
Also, I should say, I'm by no means against the use of Bayesian statistics. In fact, I think it has great value in certain apologetic contexts.
However, isn't one limitation of Bayesian statistics the presumption that the Bayesian statistician is able to assess the probabilities of a particular theory from a completely objective, impartial, and almost omniscient sort of a perspective or standpoint? As if one could comprehensively evaluate a theory on its own merits or demerits, as well as any and all unknown variables in or related to the theory?
But in practice, isn't it more often the case that one has to assess the probabilities of a particular theory in relation to competing theories?