It harms the community precisely because it's easier. A moderator will ban someone they don't like, blame it on something ambiguous they twist into a code of conduct violation, other people will point out that there's a double standard because they didn't ban someone else who broke the same rule much more clearly, pretty soon allegations of discrimination are flying.... And you also get the opposite problem where a moderator won't ban someone who's doing a lot of harm to the community because "well, they technically haven't broken the rules yet...".
Actually applying human judgement and taking responsibility for it is psychologically harder, but it's vital for moderation that's actually going to work and be respected, IME. I think we're pretty much on the same page about what moderators should actually do with what you said about "grey situations" and "spirit of the rules". But if you pretend you're following a clear written code when you're actually expecting to have a lot of ambiguity and exercise personal judgement, you're creating a mismatch of expectations that causes problems (like your example of community members micromanaging each other). Better, IME to make it clear that while you may have some agreed guidelines, moderation isn't going to be according to a legal code.