In addition to the things you mention, Fi is also about making value judgments of other people's character. Fi does not only serve to create bonds and relationships, but also to keep other people at distance if you, for whatever reason, don't like them. In that sense, Fi does involve moral estimation of other people, although the morals involved can be highly personal and totally insane, as well as totally out of sync with the morals of a specific group.
In unhealthy, unbalanced Fi-egos it is certainly possible that Fi becomes neurotic or pathological in the form of heavy moralism and/or unrelenting moral standards and hypercriticalness.