These theorems, however, ignore the issue of computation—while the best decision procedure may be Bayesian, the best computationally-efficient decision procedure could easily be non-Bayesian.
This raises another important point against Bayes, which is that the proper Bayesian interpretation may be very mathematically complex.
if we are trying to build a software package that should be widely deployable, we might want to use a frequentist method because users can be sure that the software will work as long as some number of easily-checkable assumptions are met.
I think these are the strongest reasons you’ve raised that we might want to deviate from pure Bayesianism in practice. We usually think of these (computation and understandability-by-humans) as irritating side issues, to be glossed over and mostly considered after we’ve made our decision about which algorithm to use. But in practice they often dominate all other considerations, so it would be nice to find a way to rigorously integrate these two desiderata with the others that underpin Bayesianism.
I think these are the strongest reasons you’ve raised that we might want to deviate from pure Bayesianism in practice. We usually think of these (computation and understandability-by-humans) as irritating side issues, to be glossed over and mostly considered after we’ve made our decision about which algorithm to use. But in practice they often dominate all other considerations, so it would be nice to find a way to rigorously integrate these two desiderata with the others that underpin Bayesianism.