I worked with the Wikipedia category system a few years ago, and you could see the problems with hierarchical tagging systems right in action back then. (Though it may have gotten better in the meantime)
The system appeared simple: There were just two relations, "Article A is a member of category B" and "Category X is a subcategory of category Y".
However, in practice, the community was using this system to represent a whole host of wildly different relationships between items, often with different implications what a category actually applied to.
E.g., if A has a subcategory B, this could mean one of several things: B might be an additional constraint on the items in A ("American writers" -> "19th century American writers"), the things in B might be more specific than the things in A: ("Writers" -> "Novelists"), A might apply to the concept B, not the things in B ("Occupations" -> "Writers") or A might refer to the category B ("Categories with more than 100 entries" -> "Writers") and on and on...
Of course those different aspects could even be combined. E.g. "Categories with more than 100 entries" might have a child "Categories with more than 100 entries in need of review", which represents a constraint but might itself contain less than 100 entries...
The basic question "Is item X in category Y" becomes impossible to answer generally, because there is no clear indication if a category only applies to its direct children or to all of its descendants or only to the subcategories itself.
I'm sure there are sophisticated ontological systems which would allow users to specify all those different relationships separately. I'm also pretty sure that users would become sloppy after a short time or would disagree which particular relationship to use in a particular situation...