Yes, this is a question I intend to address. As I say at the end of the post:

Also, even if one denies that the laws of physics themselves are pushing matter around, one can still believe that all the actual pushing and pulling there is, all the causal action, is described by the laws of physics, and that the non-fundamental laws do not describe genuine causal relations. We could call this kind of view causal reductionism.

I have to say, though, I don't see how saying "causality" is supposed to explain the existence of regularity. It seems like the same sort of thing as the "BECAUSE IT IS THE LAW" move I criticize in this post. If someone asks "Why do like charges always repel one another?" and you respond with something like "Because there is a causal relationship which forces the charges apart" have you done anything other than restate the existence of the regularity with some new words that sound satisfying? I guess you have also conveyed the further information that the regularity is robust under interventions, but that doesn't seem to be an explanation for why the regularity holds in the first place.

ETA: This comment might clarify what I think about the sort of issue you raise.