If A and B have different volatilities, it's rather counter-intuitive to allocate proportionally rather than just all to the one with the lower volatility... :-/

I agree, and I had to think about it for a second, but now it seems obvious. It works for the exact same reason that averaging multiple independent measurements can give a more accurate result. The key fact is that the different random variables are all independent, so it's unlikely that the various deviations from the means will line up in the same direction.

Yes, I think that's part of the point of the post. One intuition is that allocating only a little bit to a highly volatile asset creates a not-very volatile asset. Investing a little bit is the same as scaling the asset down until it's not very volatile.

The independence assumption means there's value in allocating to the more volatile one, due to diversification.