My interpretation of psychohistory is simple: it's science fiction about what science fiction itself would look like if it turned into a real science.

It has all the things science fiction does (attempts to predict the future, large scale social dynamics scenarios, etc), plus a hint of what science used to look like in the public perception at that time.

It's kind of provocative. That line of thinking implies science fiction authors need to be more science and less fantasy (exactly what Asimov himself did by starting to more textbooks and less characters).

Of course it will never exist.