Having all this can-could-may-might be called Te is getting annoying. As is the suggestion that Te is any good as an inconsistency checker or even, Lawdy, a moral judge. As is too the wonderful accretion of properties these two-letter signifiers are somehow acquiring.
Jung said that introverted feeling, like all introverted functions, seeks--and I'm going to use my own verbs here--to partake of the primordial images. It would seem he meant to suggest that all people have some similar basic psychological structure at bottom. And actually, his descriptions of both Fi and Ti are really very ugly. Those functions retain the ability to be judges by repelling and being repelled by "the object". So... seeking the primordial expressions and eschewing the object that gave rise to the seeking...
There's a great deal to unpack in that and I'm hardly sure if I have it right so far. But there is one point to make, again, about the difference between a cognitive function and, now, a value system. One is the (partial) product of the other. (And we should describe the producer in terms of the product?)
To sum up, if we don't know what Fi is, we'll be able to describe an INTJ's compassion only in the shallowest surface terms. But it'll be adorable and all.