I was too late for rdio, but from what I hear it sounds like the music service I really want :/
That was one of my main reasons for switching to Rdio when it was out, and while I really liked Rdio for its UI, it definitely had enough bugs/delays in song starting that I ended up moving (reluctantly) back to Spotify until Apple Music was released. Now, with that handled along with cloud uploads of my local media (I buy a lot off of bandcamp), it feels like a much more whole offering. I wish social and discovery features were up to Spotify's levels, but I personally have moved away from those for various reasons anyway, so it's not as much of an issue for me as it is for users who really utilize those features.
> it just lists all of the songs that I have saved from an artist, ignoring the album information
AM definitely has Spotify beat here. Click an artist, see their albums, choose an album to listen to. All in one view. It seems so natural ... I wonder if this is because I learned to curate my music on iTunes, and it is just a habit?
But for music discovery, open development practices (this is the biggest reason I switched from AM to Spotify - knowing that no matter what kind of thing I want to hack together, Raspberry Pi connected to BT speaker connected to projector, I would be able connect Spotify to it somehow), and social music experience, I think Spotify has AM beat.
Maybe I am missing something, but it seems like the flow you describe is exactly how it works in Spotify. Here is an artist page with the album list prominently featured: https://i.imgur.com/wNAjoCa.png
For example, in Spotify they just list all the tracks
https://i.imgur.com/Bse9J7z.jpg
In Apple Music, they list the albums, year, artwork, etc.
https://i.imgur.com/jyktt7R.jpg
I definitely prefer Apple's for browsing my current music.
I have a few projects too that involve the hybrid of the REST API and the libraries, it is definitely not ideal (should all be through REST API IMO). I guess Spotify could do it all over the REST API (including playback, Spotify connect, etc.), and then the client would only need to pull in a library that handles content decryption because the API can't send back decrypted audio streams (copyright/pirating). DRM is likely the biggest reason why they haven't done this yet (thoughts?), but the previous solution sounds plausible.
https://github.com/librespot-org/librespot has been a very good replacement for libspotify, and is pretty actively developed. Spotify can of course break this at any minute but it seems unlikely that this would happen.