This seems more like a move aimed at uneducated investors rather than having any chance to take off.
People want to pay a small fee per month to play any song whenever they want on any device as well as options for curated stations or stations based on their likes.
That's why Spotify took off and and iTunes continues to decline. Beats was never popular because its simply another Pandora which while before Spotify was the best option, now, all of these models fail. Why pay for Beats, Pandora, or iTunes Match, when I can get Spotify and have the best of both worlds. On Demand playing and curated playing.
Until Beats offers on-demand option it is destined to fail. Presumably it doesn't and won't offer that because then there would be far less profit for Apple. Spotify who does that model for instance has never made an actual profit. So maybe Apple hopes that eventually their business will collapse since it's not sustainable and then people will go to the next best thing which would presumably be Beats.
I assume by your post you don't realize on demand is available with Beats just like it is in Spotify.