Yes causal models are hard.

NNs do ok on those time series problems where it is really about learning a function directly off time. This is nonlinear regression where time is just another input variable.

Cases where one has to adjust for temporaly correlated errors, those seem to be harder for NNs. BTW I am talking about accuracies beyond what a typical RNN variants will achieve, which is pretty respectable. It's the case that more complicated DNNs don't seem to do much better inspite of their significant model complexity.