I'm not saying a NN doesn't reproduce analytical expressions, rather that "take everything and mix it together a bunch of times using this recipe" is not the form that the laws of nature has.
I'm not sure what you think explicit construction proves, it is clearly a case of taking preexisting knowledge and expressing it in what is doubthlessly a more akward form.
Especially since humans arguably uses wetware neural nets and don't we like to think we are coming up with causal models?
A NN can sureley result in a traditional causal model.
For example: Build a NN that has the same computational structure as some simple physics law. By giving it training data it then figures out necessary constants. That may converge to the traditional model, which is mirrowed in the network architecture anyway.
So I really can't support saying NN will by their nature NEVER be causal.