If you can create a WebGL game with some UI and soundtracks, then you can definitely create a WebGL music player, right?
In fact, if you put a bit of extra effort in, you can extend it in many interesting ways: you can add all kinds of music visualizations ("procedural music videos"), or you can create interactive content around your tracks (like Friday Night Funkin', or more subtle, like GNOG). There's nothing stopping you from doing this already on itch.io, and some people are already creating music-centered experiences.
Users can already decide to create music collections, comment and share, and you can already sell tracks.
There are some things missing that for instance Spotify has: the ability to make playlists from different creators, the whole "discoverability" aspect (like Spotify's recommendation algorithms, based on your likes), music specific tags (genres) that allow for searching, etc. However I'm not sure though whether itch.io should try to compete with Spotify this way - trying to do two things might muddle the experience and make the focus of the site unclear. And I don't think it's possible to draw the user base away from Spotify anyway. But just out of interest: which specific features would you like to have most?