No it's not "just math". You need to know what questions you're asking. You can't wave this under "do whatever works best" because evaluating "what works best"

No it's not "just math". You need to know what questions you're asking. You can't wave this under "do whatever works best" because evaluating "what works best" requires epistemology, and this is precisely what we're discussing. There are some consistency properties of Bayesianism which make it a much better candidate for epistemology than frequentism. Specifically, there are important questions in frequentism for which there are no answers. In particular, the concept of "power of a test" sweeps the prior under the rug without a proper explanation.