> Yes, broadcasting is a cool thing, but the docs mostly explains 'how' but not 'why' or 'what for'.

I'd say that, even for the 'how', thinking "OK, I have a [1, 1, 2, 2, 1] and a [3, 2, 1, 2, 5] arrays, which means that element-wise multiplication would result in a [3, 2, 2, 2, 5] array" is very useful in reasoning about broadcasting.

Just relying on simple examples and trying to build an intuition for the general case (which is the route favored in the numpy docs, I'd say) doesn't quite work, at least for me.