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.
I don't think this should be true, and if it is, then "causal inference" should be qualified to refer only to a specific modeling framework. As a counter example, it's possible to formulate a nonlinear differential equation model of Covid spread and infer the parameters to construct a plausible, causal, generative model.