We should note the limitations of Bayes as well. I already responded to another comment in this thread that giving an update procedure based on seeing new evidence is necessarily bounded in how quickly it can get you to beliefs more likely to be true by your ability to actually gather that evidence or possibly even to generate it if it doesn't already exist. We don't have any perfect algorithms for doing that, and it is of course not a purely computational problem anyway. Take general relativity. It was proposed in 1915 and only confirmed in the very strong gravitational field limit in 2016, because that was our first opportunity to observe a black hole merger, which is not something we have the ability to recreate in a lab.
Even beyond the hard process bottleneck on creating or lucking upon events that produce the evidence we need, however, there is also the limitation that Bayes only gives you a probability. It doesn't give you a decision theory or even a thresholding function. For those, you need a whole lot of other things like utility functions, discount rates, receiver operating characteristics and an understanding of asymmetric costs of false positives versus false negatives, that are often different for each decision domain.
And, of course, to get a utility function meaningful for humans, you need values. There is no algorithm that can give you values. They're just there as a basic primitive input to all other decision making procedures, yet they often conflict in ways that cannot be reconciled even within a single person, let alone across a society of many people.