And is the contemporary debate missing obvious examples of where econ theories were proven wrong or right?
Remember historians aren't an amorphous hive mind who all think the same thing, within the discipline there are supporters of loads of different economic theories, just like economists today.
I think our main role in modern economic debate is ensuring that economic history isn't misrepresented or twisted to support an argument and lay out facts as best as possible. We have to be careful when dealing with current issues though. People are very good at finding evidence to back up view points they already hold and dismissing evidence which contradicts it. Historians have a lot of historical evidence they can contribute, as long as we apply the same standards to this as we do with any historical work, historians have a lot they can contribute.
As for economic history, it's difficult to use to say one course action is definitely wrong and another definitely right. That being said there are certain economic issues where there's a general historical consensus but it's usually quite specific, most British historians would agree Robert Peel's reduction of tariffs in the 1840s was good for the economy for example. But for big questions like "how involved should the state be in the economy" history can't give you a definitive answer