Which isn't a hierarchy, it's a tagging system. The tags have some hierarchy but that's not uncommon. The distinguishing characteristic of "nested hierarchy" is that a particular thing should only appear exactly once in the hierarchy.

Since this is so terribly impossible most systems almost immediately make it possible for things to show up in more than one place, which means it's actually hierarchial tagging, whether or not the organizer(s) realize it.

You could also make a distinction based on how many tags things end up with; if it's almost always one, you could call it a nested hierachy with some exceptions, but if it's almost always more than one, and often much, much more than one, it's a tagging system. Even by that criterion that creates a spectrum rather than a binary distinction, Wikipedia is very much organized by tags and not hierarchies. I don't know what the average is but every Wikipedia page I've ever looked at the tags for has quite a few.