Expected moderation style is pretty community-dependent. In my experience it's been the other way around predominantly. Smaller communities can very much entangle moderation and the overall emotional balance among the members, especially when there's more delicate situations involved. Even in larger communities, depending on the interaction mode, moderators can be implicitly called upon as mediators, which involves a lot of trying to avoid people feeling like your response was insulting or unfair even if it was, and conversely making sure they feel like their own needs won't go unacknowledged.

In larger, topic-oriented, and/or highly generalist communities, ones that are looser and more impersonal in general, it's been more as you describe.