Maybe because useful time-series modeling is usually really about causal modeling? My understanding is that mediated causality in particular is still very difficult, where adding extra hops in the middle takes CoT performance from like 90% to 10%.

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.