I believe DAG-based causal inference isn’t able to handle feedback loops (acyclic) or nonlinearity (linear). Nonlinearities include stuff like deadbands and delays.

Control theory models handle these things just fine. But control models are hard to apply to sociological/epidemiological domains, where causal inference dominates.

From what I gather, causal inference is useful for designing studies. I’m not sure if they’re used for prediction — would appreciate if someone in the know could chime in.