According to Appleinsider, Apple has acquired the license to stream music but chose not to because it fears that the wireless networks would not be able to handle the load. And given Apple's experience with AT&T, who would blame Apple.
This is how Apple works and why it'll always have its core fanboys – and by most reckoning, it is a bigger number than ever before. While other companies don't have this problem about preserving quality for its customers, Apple would rather forgo the revenues if a service doesn't provide a certain level of quality. Personally, I'm pretty easy to satisfy. I've tried Rdio and it seems fine to me.
And I rather own my music than "rent". I think a lot of people share this opinion Now, when it comes to video, that's a different story. I have both Netflix and Hulu Plus. So, Apple, if you want to offer a video streaming service with a big library, I'm ready to sign up.