I am speaking in terms of IxxJ and IxxP types here just for clarity: I think a lot of it comes from the fact that Pi functions need to be filtered. Stand alone unprocessed, what they bring to the table is pretty much useless. The way in which they need to be processed is very J most of the time.
The inverse is for Ji functions. They are by their nature J oriented, but more or less useless (though not nearly as pronounced as it is with Pi functions) stand alone. Unlike Pi functions, it can be used, but it's often not. They need to be processed, and the way in which they are processed is inheriently very P.
Really, for introverted types, their primary function, while either P or J, actually shows up differently because of the needs of it. That's ultimately what shows up externally, because it's what introverts are trying to do, that ends up showing.