The not-actually-calculated form of Bayesianism that seems useful to me is the reminder that statistics aren't calculated in a vacuum. For example, for the hypothesis "the moon landing was faked" to be true, other things that would also have to be true include that the USSR would pretend to have lost the space race, and that large numbers of people could keep a secret for years, for no apparent benefit to themselves.

That may be so much Bayesian priors as Bayesian consequences: if X remedy sold as homeopathic works, either it's working for non-homeopathic reasons (or a lot of the rest of medicine and science has to be reexamined as well. And most of the time people aren't going back to those first principles, they're saying "there's no evidence this works, and lots of reasons to think it doesn't, one of which is that the postulated mechanism makes no sense and would require us to reconsider a lot of other science." But they didn't start at "here's why Avogadro's number matters" rather than "why aren't the homeopathic remedies that people pour down the sink affecting the biosphere?"