Ideally these communities would be prevented from appearing in the “Trending Communities” list or local/global feeds unless someone other than the owner was subscribed to them, but wouldn’t be private in the sense that no-one could see them. Just they wouldn’t get wide distribution.

This raises a distinct but interesting additional feature request that might complement "private" or exclusive communities, as well as others that might like to prepare a community before promoting it: a hidden or unlisted setting for communities.

That would enable what you mention here, preventing their appearance from trending, and perhaps also user profile/data areas (i.e. if one can indirectly view others' subscriptions, this might offer a way to obfuscate/hide that from others besides admins).