I don't think it's second-order good epistemology trying and succeeding to counter bad epistemology.

Let's say we run a study with 30 people, and we conclude ZM's method is the best, with p = .55 (sorry, I don't think in Bayesian when I have my psychology experimentation cap on), which is realistic for that kind of sample and the variability we can expect. Now what?

We could come up with some kind of hokey prior, like that there's a 33% chance each of our techniques is best, then apply that and end up with maybe a 38% chance ZM's is best and a 31% chance mine and Pjeby's are best (no, I didn't actually do the math there). But first of all, that prior is hokey. Pjeby's a professional anti-procrastination expert, and we're giving him the same prior as me and Z.M. Davis? Second of all, we still don't really know what "best" means, and it's entirely possible different methods are best for different people in complex ways. Third, I don't trust anyone including myself to know what to do with a 7% chance. I like my method better; should I give that up just because a very small study ended up shifting the probabilities 7% toward ZM? Fourth of all, we still wouldn't know how to apply this to picoeconomics as a theory: using any technique will increase success by placebo effect alone, we have several techniques that all use picoeconomics to different degrees, and we would have to handwave new numbers into existence to calculate things and probably end up with something like a .1% or .2% shift in probabilities.

And this is all if we have perfect study design, there's no confounders, so on and so forth. It would take a lot of work. The best case scenario is that all that work would be for a single digit probability shift, and the realistic case is that there's flaw somewhere in the process, or we simply misinterpret the result (my guess is that people can't deal with a 2% shift correctly and just think "now there's evidence" and count the theory as a little more confirmed) then we'll actually be giving ourselves negative knowledge.

I'm not saying Bayes isn't useful, but it's useful when we have a lot of numbers, when we're willing to put in a very large amount of work, and where there's something clear and mathematical we can do with the output.