Ti and Fi can't do anything without data from N or S. N and S perceive a picture of a web of words/concepts/relations that T and F check for consistency (external consistency for Je, internal for Ji).
there is no "knowledge" of self without all 4 functions working in tandem.
Well, yeah that's kind of obvious. Nothing really works without P-J intereaction.
introverted perception is great for self-awareness because it filters through data automatically and only focuses on data that relates to the self. Fe can check whether or not that data is "good" according to the external standard. so an INFJ would be quite good at seeing how they fit in (value-wise) to their surroundings. Fe doesn't even have that much work to do since Ni only has data that focuses on the self anyway.
What does the external definition of good have to do with this? And what about fitting in?
judgment doesn't "understand" any more than perception. understanding takes 4 functions.
it's really hard to say which function combination is best for self-awareness. they all understand themselves in different ways.
i do believe, though, that NFJs would be the best at guessing how others perceive them. if self awareness is defined by how close the individual gets to the common view of themselves, Ni/Fe is probably the best.
This "different ways" things comes back to the main issue. We clearly haven't been settling on a single definition of of self-awareness or even "understanding" apparently.
I can say that self-awareness, and especially self-understanding, in my mind, had nothing to do with knowing how others see you. I'd hate to based the defition of the self on common, outside perception. I think that knowing one's own value system, both factual and sentimental, is the closest thing to self-understanding. That clearly puts Fi and Ti over Fe and Te.
Perception will be necessary to gather information about the self, of course. I suppose Ni is being picked because we can assume that Intuition is more self-originated than Si? Either way, Perception alone wouldn't be good enough of course, as only the Judgement actually makes sense of the information. Only the Judgement actually creates something comprehensive from the information. So, maybe that makes Pi and Ji even in this comparison, because Perception will never really create the understanding, but it is pre-requisite for the Judging to take place at all.
The conclusion I gather here, though, is that the most self-aware type is one that doesn't exist according to the MBTI. It's something to the effect of NiFi.