For example, my music collection is big and diverse, and both "year sort" and "album sort" are kinda useless now, because there are actually multiple disjoint subsets. There is no point ever in showing me audiobooks for year 2010 and regular music for year 2010. I always only want a subset of it.
This is what I meant "strictly in addition to main hierarchy" -- let me keep my folders, and maybe when I want to go deep enough, I want to browse by tag. But even then it would not be a hashtag-like tags that the original page refers to.
Artist sort, year sort, genre sort, etc. Genre is really hard though.
There isn't much reason to use tags as the only way of organizing things though, they work great as views.