I fear you operate under the illusion that frequentist statistics are somehow limited to hypothesis testing. It is absolutely not the case.
I wonder if the generality of the Bayesian approach is what's prevented its wide adoption? Having a prescribed algorithm ready to plug in data is mighty convenient! Frequentism lowered the barrier and let anyone run stats, but more isn't necessarily a good thing.
1. They aren’t answering the original question. The question is about the probability of a property of Saturn. Not about the process of repeatedly forming thousands of alternative Saturns. This seems like a subtle difference but that’s only because Frequentism has been the default for so long. It doesn’t attempt to answer the questions people are actually asking.
2. The assumptions it makes to answer that alternative question are just as flawed. We can’t go back in time and change the conditions surrounding Saturn’s creation. We can’t run 1000s of repeated trials of the creation of Saturn. For a group of people so ideologically opposed to a statement as simple as “the probability of this flipped coin being heads is 50%”, it seems absurd that they are fine with their entire framework being built around a premise that doesn’t exist and cannot exist.
Yes, I think this is kind of standard practice in many fields.
If someone questions this just quote "all models are wrong, but some are useful" as if the quote is actually saying "all models are wrong, but all models are useful".
That isn't much of an argument to the mathematicians. Nobody ever came up with a compelling explanation for what -1 sheeps look like and yet negative numbers turned out to be extremely practical. If it is absurd and provably works then the math community can roll with that.
Math people prefer to generalize. But with frequentism, it is not possible to generalize because "frequency" is baked into its very name. Indeed you can imagine Bayesian statistics as the generalization of frequentism.