I'm going to sound like an Apple apologize, but what's wrong with Apple Music on the web? I just launched it (for the second time in a while), and after signing in, was presented with a familiar looking UI and all my playlists, and was playing searched-for music in under a minute. I know Apple prioritizes their platforms first, but this doesn't seem like an example of Apple failing a competing platform.
Apple Music on Android is actually really good, I use it daily. On some level it was a priority for them for market share, to compete with Spotify. I don't see the "competitor" in this space (cloud) though that would drive that necessity.