> Interestingly, when I see Bayesians simulate random data (to introduce the concepts on this data) they usually assume a true parameter value. E.g. when sampling from Y = a + b * X + e, they'll assume fixed, true values of a and b and not random variables - which is a frequentist assumption! So far I've never seen e.g. b being sampled from Normal(mu=2, sigma=1) instead of just setting b=2.

The Bayesian philosophy of "random parameters" does not mean that Bayesian methods cannot be assessed for frequentist properties or compared against frequentist procedures.