Econ is an interesting subject. Basicaly, it's taught using slide-ruler-y math from the 1950's[1]. Its amazing that learning to build linear algebra models without a slide-ruler (ie, by hand), comined witha year or two of statistics and some calc, makes someone an expert in "Economics".
If you think about the huge increase in computer power available today, it seems a field ripe for disruption. However, the guys that run the fed, and guys like Krugman are basically from the "slide rule era" of Econ.
I'm sympathetic to the power of modeling and techniques, but I do think its a case of the more you know, the more you understand what you don't know. And I think for most people the deeper you go into the field of Econ, the more this becomes apparent. Its getting better, though, and I'm sure in another generation (once the current tenures expire) things will look a good deal different (hopefully better).
Not sure if your views are similar, though.
[1] You see no little to no respect for dynamic systems that are chaotic or non linear; bounded rationality and its antecedent effcts; the role of institution underpinnings to markets, etc. Just to name a couple that are glaringly relevant and empirically important, but not subject to "hand math".