Asimov's psychohistory is just the MacGuffin that drives the story. The Second Foundation is the control mechanism. It doesn't just correct for the effects of mutant outliers like the Mule, but also the development of new technologies. IIRC, Asimov's final retrofit was that Galaxia was the goal all along. The Spacers were central to this plan, although they don't appear in the original trilogy as far as I recall. That they are prominent in this series suggests they will play an increasingly important role.
Real-world
psychohistory is largely considered a pseudoscience by social scientists, historians and anthropologists. Perhaps its proponents need to start adding some mathematical methods from macro- and microeconomics. For example, the development of psychogenic modes is probably directly related to improvements in economic conditions. However, I doubt that modelling human populations using macroscopic variables would ever provide anything more than broad indicators of trends. Paradigm-shifting new technologies are always going to throw a spanner/wrench into the machinery of prediction.