> What I want, is button, when I press that, "The Almighty Algorithm" will analyse the sound, the beats per second, the vocals, the instruments, the lyrics, anything that affect the sound and locate other songs with similar profiles. Bonus points for letting me input stuff like: higher tempo, less bagpipes, the singer has a high pitch voice which hurt my ears.

This might be possible in theory but part of the issue is that the algorithms input parameters are not the same from person to person. The parameters you described are mostly technical attributes of the sound, but what about cultural/political affiliation? Do you care if the lyrics are in a different language (some people do, some people don't). Do you care if there is a political or religious message (and are you particular about which religion or political tribe)? Can Spotify take that into account somehow? Maybe, but it seems very difficult to tailor that to the user.

Speaking personally, music is more than just an aural experience for me. At times it's about connecting with my social group, or cultural traditions, or a spiritual experience. At other times it's just the music. When I listen to mainstream stuff, Spotify is ok. When I get deeper into edge-case territory, Spotify doesn't really know what I'm looking for and often makes suggestions that appear to demonstrate a shallow understanding the cultural meaning of the music I'm listening to.