"Cache" implies they're only temporarily on your device. This is false: the files are downloaded and encrypted on your device, and do not go away unless you explicitly tell Spotify/Rdio to remove them.

Spotify/Rdio will remove those files at any time if they lose the license to play them. This is not the case with media files you own, and have complete control over (lacking DRM).

Caching it on the device is enough for me. I'm fine with knowing that I don't really own my music, as long as I can still listen to it while I'm on the subway without cell signal.

Google Play will let you pin music to your device from their streaming connection. That keeps them around until you unpin them.