The need for a power analysis in a clinical trial for example is to be able to calculate/estimate how many participants to recruit to have a chance of finding a treatment effect (of a given minimum size) if it exists. It isn't feasible to recruit an endless number of patients, first because of time constraints and second because of cost constraints.
So, imagine we are taking a Bayesian approach to said clinical trial. Although flat priors are in theory possible, sensitivity to the prior is advisable anyway since, unfortunately, more than one flat prior is available (which is odd I'm now thinking, as really there should only be one way of expressing utter uncertainty).
So, imagine that, further, we do a sensitivity analysis (the model and not just the prior would also be under scrutiny here). This involves simulating from a plausible model for 'the truth'. In classical/Frequentist statistics, there are four candidates for 'the truth' here: H0, mu=0; H1, mu!=0 where either are observed with error (as in our real world), or without error (as in the unobservable real world). In Bayesian statistics, there are two candidates for 'the truth' here: mu is a random variable (as in the unobservable real world); mu is a random variable (as in our observable real world, from an uncertain individual's point of view).
So really it depends who you're trying to convince A) by the trial and B) by the sensitivity analysis. If it's not the same person, that would be quite strange.
What is actually in question is a consensus on what truth is and on what substantiates tangible evidence. The shared ground is that signature probability distributions are observable in our real observable world that do in some way evidently have some underlying mathematical truth that just happens to be so by chance, or is by design. I will stop there as this isn't an Arts page, but rather a Science page, or that's my understanding.