No problem of course. But that's a big if. And how are you going to evaluate whether both methods do in fact deliver the same answer?
Also, the Frequentist approach is not wrong. It's inaccurate, to the extent its results differ from the Bayesian ones. This inaccuracy tend to go down as we gather more data. Which is a good thing, or else science itself wouldn't work.
One more thing. You said "in some sense". Are you seriously suggesting that the assumptions behind Cox's Theorem can reasonably be challenged?
I'm ashamed to say that I said "in some sense" to be deliberately vague about what I meant by consistency - I didn't want to overstate the strength of Cox's theorem or end up arguing about Godel.
Also, the Frequentist approach is not wrong. It's inaccurate, to the extent its results differ from the Bayesian ones. This inaccuracy tend to go down as we gather more data. Which is a good thing, or else science itself wouldn't work.
One more thing. You said "in some sense". Are you seriously suggesting that the assumptions behind Cox's Theorem can reasonably be challenged?