Reproducibility trumps causal models. If you call the psychic hotline and get the same results time-after-time, then keep using the psychic hotline. Leave the modeling to others.
When developing new science, stats lag behind reproducibility. First you see something that correlates, then somebody is able to make A always infer B, then you start doing some statistical surveying in an effort to build up a larger model.
Observation first, then Abduction (in the Peircian sense), then measurement, then modeling, and finally Deductive/Inductive reasoning.
We keep trying to do it backwards where we have the model for everything, then bang actual data into various parts of the model. The saddest thing in this process is that if we're only doing incremental, normal science (Kuhn), none's the wiser. This is why reproducibility tests are so important. We lie to ourselves. We're quite good at it.
BTW, I agree that with you general conclusion about case analysis and such, but only in the sense that it drives Abduction, not as a goal in itself.