Keep in mind also that the regression-based adjustment works only for linear models, which involve a major modeling assumption. With linear models, we lose the ability to model nonlinear interactions, such as when the effect of X on Y depends on the level of Z. The back-door adjustment, on the other hand, still works fine even when we have no idea what functions are behind the arrows in the diagrams. But in this so-called nonparametric case, we need to employ other extrapolation methods to deal with the curse of dimensionality.
