I'd rather know Shiller's ideas on how to throw out the bad ideas in the public consciousness than if his field of study will make it in the long term. Policy is too often treated more like a religion than an implementation of tested ideas.
I think that the verifiability problem in economics is, however, more pernicious than that for other sciences precisely because of the subject area which it addresses, namely the economy. The standard of evidence for the implementation of some economic policy is, quite generally speaking, vastly lower than for the application of other scientific advances, and the impacts of either can be large. This means that unverified or even unverifiable policies can quite easily be implemented in the real world, and then cause significant damage, as steauengeglase mentioned.
If we are incapable of verifying that a given policy might work, because the theory it is derived from is so incomplete as to ignore the things which might cause the policy to fail, then why should we consider that policy's adoption? It is surely far more sensible to generally apply well-tested ideas, and conduct small-scale policy trials to expand our knowledge.
The obvious problem with this latter approach is that the "well-tested ideas" are very often derived from distinctly inequitable modes of thinking. I would still contend that adopting and then adapting those ideas is preferable to applying radical ideas that ignore most of the system they purport to explain.