Functionally, for the consumer, streaming is mostly identical to a recording. Want to listen to a song? Press play. The storage just happens to be on some server somewhere.
Would I pay a streaming service $10 a month for 10 tracks, that I can only listen to on their service, but which I get unlimited plays of so long as I subscribe to their service? Hell no.
Would I purchase an album of 10 songs, that are mine into perpetuity to listen to, make reasonable copies of, fair use of, etc, for $10? Yes.
Would I pay a streaming company for on demand access to a broad catalog of songs? Yes.
But note how my consumption and value varies.
The thing is, streaming services are, fundamentally, gainining 'per listen' value, and that model is reflected into how they're paying rightsholders. That is, the more I listen to a track, the more value it collects for the owner.
A purchasing model is how many purchases. Listens are not really correlated to that (at least, not to the price). That is, one user may listen to the purchased album 100 times, the other may listen to one song 100 times, and one user may listen to the album 1000 times. All paid the same, all generated the rightsholders the same.
As such, I think treating streaming as a storage medium would be...poorly thought out. Not least of all because at that point you could make a strong case that the streaming service should be paying every rightsholder for every subscriber; they are, after all, -storing- that music for the new subscriber; nevermind if the subscriber ever listens to it or not.
I permanently have the right to listen to a CD I own as many times as I want.
With Spotify, as far as I'm aware, they can yank any part of the catalog without anything owed to me as a listener. If I wake up tomorrow and the only thing available is John Cage's 4'33", I have no recourse. Spotify isn't offering me storage space.
Perhaps, more importantly, it's easier for Spotify to enforce this, than a CD-making company.
Otherwise, you could just legally extract the bits downloaded onto your computer and keep the music files you have just streamed from Spotify or any equivalent service.
I think the reality is that over 20 years after the development of Real Player, we still don't have a good legal framework to discuss streaming.