What is a time limit? Do actual bets on this sort of thing in Britain stipulate a time limit? As a Yank, I have no idea how betting 'markets' like this like this actually work.

Not really. To the extent that we limit attention to theories of the form:

Always(Everywhere(Forall x (P(x)) ) )

we Bayesians can never "cash in" on a bet that the theory is true - at least not using empirical evidence. All we can do is to continue trying to falsify the theory by experiments at more times, at more places, and for more values of x. As Popper prescribes. Our probabilities that the theory is true grow higher and higher, but they grow more and more slowly, and they can never reach unity.

However, both Bayesians and Popper fans can become pretty certain that such a theory is false - even without checking everywhere, everywhen, and forall x. Popper does not have a monopoly on refutations. Or conjectures either, for that matter.

The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses - uncertainty about all beliefs, in fact - and it works just great.

Really? No exaggeration?

Sure, we could go back to the dark days before Bayes, and struggle on with a boolean conception of certainty, and it probably wouldn't be so bad that it would acutually prevent knowledge from growing...

Popperian epistemology was created in the 20th century, after Bayes, so what do you mean by dark days. Certainty is not the lynchpin of knowledge creation and in fact has nothing to do with it. You completely devalue the role of explanations and criticisms. Who cares about probability when you have a good explanation that has withstood criticism?

...but what possible reason would motivate us to take such a retrograde step?

Popperian philosophy is about problem-solving, explanation and criticism and these things are not in any way retrograde. Bayesian epistemology is rooted in the old philosophy of justificationism, a philosophy that Popperian epistemology overturned.

I mean: how do you model equiprobable competing theories in such a framework.

What you do is attempt further criticism of these theories and if that doesn’t progress come up with a meta-theory of what to do giving that you have two good candidate theories. It is always possible to come up with such a meta-theory.

How do you model induction? How do you model confirmation?

The answer seems to be that you don't - you just deny the very existence of these phenomena!

Popper and others have given explanations - they don’t just deny without reason. Are you familiar with their arguments? There are real problems with the very concepts of induction and confirmation, problems that you seem not to have appreciated.

I hope you can see how that is not a step forwards, from our point of view.

Popper showed that knowledge grows perfectly fine without concepts of uncertainty, induction, and confirmation. Yes, it is counter-intuitive - that is why most people do not get Popper.