I would describe this breakdown as misleading at best.
Frequentists are not a special case of anything. Standard frequentist arguments make absolutely no sense from a Bayesian perspective. For instance there is no prior in which such a thing as repeated significance testing errors can possibly exist. Conversely frequentists can legitimately point to a lot of things that Bayesians do which are at best highly questionable. Such as picking a default prior that gives massively high probability to clearly unlikely scenarios. (Yes the Bayesian replies, but we could pick better priors. But, the frequentist retorts, in practice you don't.)
I think that it is best to learn both, then do whatever makes most sense for your circumstances.
Frequentists are not a special case of anything. Standard frequentist arguments make absolutely no sense from a Bayesian perspective. For instance there is no prior in which such a thing as repeated significance testing errors can possibly exist. Conversely frequentists can legitimately point to a lot of things that Bayesians do which are at best highly questionable. Such as picking a default prior that gives massively high probability to clearly unlikely scenarios. (Yes the Bayesian replies, but we could pick better priors. But, the frequentist retorts, in practice you don't.)
I think that it is best to learn both, then do whatever makes most sense for your circumstances.