> You could also scrobble your own mp3s but (as I remember it) the whole point of that was so you could then listen to the stream tailored

That's not how I remember it at all. The biggest features (that at least made me and my friends use it) was that no matter what player you used, it probably had a "Scrobble to last.fm" features (which sadly, seems Spotify at least removed), and then you'd use Last.fm to find new songs to play via your own player.

I don't think I remember anyone using the Last.fm radios/playlists, but instead just as a data-browser to find new artists/albums/songs, then play those somewhere else.

But this was around 2005 sometime in Sweden, we basically just had Spotify and maybe Grooveshark available for streaming, maybe things typically worked differently elsewhere.