My point was that 'probability of minted coins' isn't a much "smaller-scale" question than 'probability of Alexander', that is, it isn't much simpler and easier to decide.

In our model of the world, P(coins) doesn't serve as a a simple 'input' to P(Alexander). Rather, we use P(Alexander) to judge the meaning of the coins we find. This is true not only on the Bayesian level, where all links are bidirectional, but in our high-level conscious model of the world, where we can't assign meaning to a coin with the single word Alexander on it without already believing that Alexander did all the things we think he did.

There's very little you can say about these coins if you don't already believe in Alexander.