In fact the system I've created as a testbed works by storing a many-to-many tag-filename mapping. However my contention is that hierarchy can be modeled as a subset of tags. Tags are conceptually more powerful and should be the interface exposed to users, not hierarchies.

That hierarchies can be expressed by tags is easy to demonstrate. Simply tag each file with all of it's parent directories up to root. Implementing hierarchies in terms of tags is not as computationally efficient, so you wouldn't actually write a filesystem in that way. The point is to create a new interface for humans, not for software. When a human has a dataset that is genuinely best organized as a hierarchy, they can express that hierarchy in terms of tags.

Of course traditional file hierarchies implemented in the traditional way, not in terms of tags, must still exist for some purposes. Source code, which requires a deterministic and efficient way to refer to specific other files, is one example. (However the user could still benefit greatly from augmenting the source code tree with tags.)

What I'm suggesting is not that hierarchical file systems be removed from operating systems, but rather that they be removed from nearly all user interaction with computers. The "Save as" dialog should not be exposing the hierarchical file system, at least not by default. Ditto the "Open" dialog. Hierarchical file managers like Finder, Explorer, Dolphin, Nautilus, etc should all be revised to be foremost file tagging systems designed to aid the user in managing and querying their tags. The "Desktop" should not be a directory on the filesystem, but rather a tag (or even a complex dynamic query.)