I agree that probably most people running regressions (in economics at least, I don’t know about other disciplines) are either explicitly or implicitly trying to estimate a causal effect, and this usually seems to be the motivation for including controls. The exceptions would include prediction; summarizing the data; estimating a non-recursive system where the coefficients on endogenous variables don’t have a causal interpretation; rational expectations econometrics (e.g. Euler equation estimation) where the conditional expectation being approximated is that of the agents in the model and the parameters being estimated (e.g. the elasticity of substitution) have at best a rather complicated causal interpretation. And yes, it’s true that if you were using regression to approximate E(Y|X1) you wouldn’t need controls, you would only need controls if you want to approximate E(Y|X1,X2,…) (in which case, the coefficient on X1 is the change in the expected value of Y as we move from one observation to another observation with a higher value of X1 and the same value of X2, etc.).
Judea Pearl argues that we should emphasize as strongly as possible the difference between these two interpretations of linear equations (conditional expectations and causal effects) – I am neither a statistician nor an econometrician but I find his arguments persuasive. Of course, economists do already worry a lot about endogeneity, but this doesn’t mean that they are always clear about what `causal effects’ they are estimating (i.e. precisely what hypothetical interventions they have in mind, what is being varied and what is being fixed), at least, not in macro. One way to fix this might be to emphasize that what regression gives you, in the first instance, is an approximation to E(Y|X). A causal effect is something conceptually completely distinct from that, and you might or might not get it from a regression. If memory serves, my textbooks were clear on the first part (regression gives you the CEF) but vague on what a causal effect was.
Anyway, my main point was that it might be useful to keep the conditional expectation interpretation of regressions in mind especially if you think many interesting questions are descriptive rather than causal (though to be fair, if you want to approximate the CEF, there might be better ways than linear regression).