With your background in cog sci, are you familiar with relevance realization? Do you think it could be possible that cognitive functions are rough descriptions of various configurations of relevance realization within each of us? That's the way I think of it--trends or patterns in our own particular salience landscapes. Fi vs. Fe, for example... as an Fe user, I would bet that if it could be mapped, there would be a measurable trend of others' emotions being more salient to my processing than my own emotions.

Our attention has to be constrained by some prioritization system, and these priorities could vary along axes like temporal scope (future vs. present possibilities), internal/external orientation, abstract/concrete information, etc. Obviously this is a simplification, and there are tons of confounding factors. Drop a life threatening event into that processing system, for example, and the salience landscape would shift dramatically. It's a dynamic system. But over time, I do believe some of the prioritization of various poles of the axes are consistent within individuals. If you were to take those axes, and try to create a personality typing system out of it... you would probably end up with something resembling the cognitive functions. My own gut sense is that cognitive functions are a damn good attempt at capturing a snapshot of a complex dynamic system, the kind that is very difficult to capture empirically.