Well, it's less of a technology problem than it is an industry one. You can have multiple entries in the genre list and they're freeform, for example Ambient;Electronic, in both ID3v2.3 and ID3v2.4. For Vorbis Comments, you have multiple GENRE= tags. Some players support this.

In my interactions with distributors, it seems streaming services tend to support up to two genre classifications; though they're pretty outdated and general (even more general and dated than the Winamp genre list). I don't think they use the metadata presented much in the classification; in fact Spotify does its own estimation of 'energy' and other subjective emotions using various classifier algorithms.