This isn't just about a difference in the choice of loss function to optimise. It's a difference in what sort of guarantees you seek about that loss function.

This isn't just about a difference in the choice of loss function to optimise. It's a difference in what sort of guarantees you seek about that loss function. Bayesian analysis seeks an estimator which minimises posterior expected loss, conditioning on the data and with the expectation taken over the parameters under a particular prior. A frequentist analysis might seek an estimator for which uniform bounds on the worst-case expected loss are available, which hold in expectation over the data, given any value of the parameters. Both approaches fit into a decision theoretic framework and there are good reasons why you might care about frequentist properties when making decisions. I agree that this isn't only about average case vs worst case -- as you point out it's also about whether you take expectations over data given params or over the params given data, and that's important too. But I think the average case vs worst case aspect of this is an important part of what this is all about and gets to the heart of what the trade-offs are when choosing between these methods. I disagree that the sampling distribution is "irrelevant for making decisions", that's quite an extreme view which I don't think many applied Bayesian statisticians would take. Frequentist properties are something people often validly care about when deciding on a statistical procedure to use in an experimental design context, i.e. before collecting the data -- and especially if you're choosing an estimator which you intend to use many times for many experiments, even if they're not all exact replicates of each other.