In fact, Microsoft was one of the first major players in the streaming subscription market. Before Google Play Music Pass, before Spotify, there was the Zune Pass. It was a sweeter deal back then, $10/mo for all you can eat and you got $10 in credit for songs every month that you could keep even after you cancelled your subscription. Basically pre-pay for 10 songs every month and you get the entire streaming catalog.
Rhapsody was the only competitor at the time that I knew of. The Zune Pass service didn't really catch on because, well... you needed a Zune.