The music site Magnatune (http://magnatune.com) does that.
They split your money into two piles, one for downloading (you can download anything you want) and one for streaming.
While I don't know exactly how magnatune works, what you've described is completely different from what I've said, unless your streaming pile is distributed only among artists you streamed, and not put together with everyone else's money and distributed among all artists.
Having just superficially perused Magnatune's info pages, I couldn't find anything specifying how they determine the amount given to artists, other than 50% of it goes to artists, and the other 50% goes to Magnatune...
Having just superficially perused Magnatune's info pages, I couldn't find anything specifying how they determine the amount given to artists, other than 50% of it goes to artists, and the other 50% goes to Magnatune...