One-to-one mappings between Enneagram types and Jungian functions is mapping apples to oranges. If you have 15 apples and 15 oranges, that doesn't make apples the same as oranges. Yes, there are many personality aspects of type 9s that seem Si, but they tend to fit Ni and Fi rather well, too. Check out Z's chart from a while ago:
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[Caveat on this data - type 9s are notably more rare in online forums such as these than as tested in real life, so these data are necessarily skewed by the population sample. Even so, it should be clear that the correlations are just that, correlations, and not arising from a common cause.]
In general, it's the IxFx type that identify as 9s, just as the ExxPs that tend to identify as 7s. Type 4 would appear to be Fi, as you say, but that doesn't explain why it's a top choice for INFJs. And type 6 would appear to be more of an Si type, as both Si doms have it as a top pick (though it would appear to be more of a "J" thing, than Si). The only one that is close is the type 5 with Ti association, as that's a fairly significant correlation, but even with type 5s, it would appear that it is more of an IxTx thing than a Ti thing.
The only things that are similar here are the personalities, not the typologies. The personalities are the
results, the typologies are the means of arriving at the results.
One of the reasons I appreciate Enneagram now more than I did a while ago (thanks Z!) is that it's so completely
orthogonal to MBTI. MBTI and cognitive functions have no bearing on neuroses, while Enneagram categorizes all sorts of varied coping mechanisms. That very orthogonality should give the lie to associating specific functions with specific Enneagram types.