Maybe the problem is that "relationships more complicated than linear sensitivity to single variables" are hard to study scientifically, and Western medicine is supposed to be founded on science.
That's true in a practical sense today for most scientists, but it need not always be so.
Multivariate linear regression is currently the swiss army knife of the statistical sciences. Even now there isn't much appreciation of its merits, flaws, applicability and power. But now that we have computers powerful enough to interactively process and visualize data, it seems to me to be possible to bring an understanding of non-linear statistical modeling.
