I do want to note that there's no contradiction in the mathematics between Bayesian and Frequentist - you don't get different answers and both are based on the same underlying theory of probability (which at its ultimate is based on a Lebesgue Measure, though applied statisticians never have to concern themselves with that).

This is not to contradict what you are writing - these are two very different outlooks. But I do want to reassure people that there's no controversy of the math path.