Forty roles gives you 0.9999999999999999999999999999999999999999, a confidence so high it is forbidden to a Bayesian under any circumstances.

Why? You have explicitly assumed a prior distribution:

You have two competing hypotheses:

• The ten-sided die is fair. It produces the numbers {1,2,3,4,5,6,7,8,9,10} with equal probability.

• The ten-sided die is weighted. It always produces the number 10.

Actually, you have not specified what probabilities the Bayesian is assigning to these two. Suppose for the moment that it is 50-50.

It is straightforward to combine this with the observed die rolls according to the Bayesian calculation. If the Bayesian is not willing to bet at the resulting odds, that only means that that was not his prior. Bayes' Theorem does not depend on anyone's actual belief about anything.

You omit to say how the Frequentist "bur[ies] wrong beliefs under a mountain of data". Presumably you believe that the data in this example has done so. But what is the Frequentist's argument? "Lookit this mountain of data!"? Actual papers doing statistical reasoning never have such mountains, especially in reproducibility-crisis fields.

I am not sure I understand, probably because I am too preprogrammed by Bayesianism.

You roll a d20, it comes up with a number (let's say 8). The Frequentist now believes there is a 95% chance the die is loaded to produce 8s? But they won't bet 20:1 on the result, and instead they will do something else with that 95% number? Maybe use it to publish a journal article, I guess.

I don't think my first Bayesian critique is "nine nines is too many"; there are physical problems with too much Bayesian confidence (eg "my brain isn't reliable enough that I should really ever be that confident"), but the simple math of Bayesian probability admits the possibility of nine nines just like anyone else.

I think my first critique is the false dichotomy between the null hypotheses and the hypothesis being tested.

Speaking for the frequentist, you say:

If you roll the die nine times and get nine 10s then you can say that the die is weighted with confidence 0.999999999.

I don't think this is what a real frequentist says. I think a real frequentist says something more like, the null hypotheses (the fair-dice hypothesis) can be rejected w/ that confidence. Specifically, the number you are giving is 1 - P(evidence|fair). This is not the numerical confidence in the new hypothesis! This confers some confidence to the alternative hypothesis, but that's better left unquantified, particularly if "falsification is the philosophy of science" as you say. We don't confirm hypotheses; hypotheses are rejected or left standing.

But whether you wear your heart on your sleeve by naively stating that nine nines is the confidence in the new hypothesis, or carefully hedge your words by only stating that we've rejected the null hypothesis of fair dice (and haven't rejected the alternative, wink wink), still, my critique of the reasoning is going to center around the false dichotomy. Frequentism makes it too easy to bury mistakes under mountains of evidence, because it's too easy to be right about what's wrong but wrong about what's right.