Something semantic would seem better, yes.
I disagree. The feature isn't specifically about administrative categories, it's about hidden categories, so HIDDENCAT makes sense. You could have an alias, I suppose.
Are there other meanings for which you'd want to hide the category?
Who knows? People use Mediawiki for all kinds of things.
And should stub categories be hidden by default?
Does the phrase "stub category" have any meaning to the software? Aren't they just like any other category? In which case, whether or not they're hidden is a matter for individual wikis.