Actually, Bayes statistics works great in poorly defined problem spaces where we can update our priors as new information becomes available. Just like in the issue under discussion.
Your example of rolling dice is Frequentist, not Bayesian. We wouldn't use Frequentist stats in this domain, for the reasons you mention.
Can you give me a few comparable scenarios where it worked great?
I don't know whether Bayesian search is currently being used to search for the unknown reservoir species from which SARS-COV-19 jumped to infect humans (assuming a natural cause).
Under this approach, the longer the search goes on, the more we may lessen our confidence in the prior assumption that it was a natural infection.