The use case is the same as for the lock icons, which, I think, is to remind users: if you post here or share a link from here it won’t be accessible by everyone.
I feel like I don’t need that reminder for login-only categories, because very few categories on my site are visible to anonymous users. (Instead, I mark the publicly visible category’s with an icon to remind users that these are out in the open internet.)
For categories that have more restrictions than “must be logged in”, it can be less obvious that they’re for a more or less exclusive group only. New users might have been granted access to a group when they first created their account. So from day one they’re seeing a different set of categories than some other users, but unless the category name or description (if they read it) includes a hint, they couldn’t tell that a category is visible only to some. Older users might forget that this one category they once were granted access to is not in fact accessible by all.
So, in short, a quick visual reminder like the lock icon makes more sense to me for restricted categories than applying it to almost all categories on a mostly logged-in only site.