There's another option, which is to calculate the "per play" rate differently for each listener. If one user plays 300 tracks per month (one 10-track album per day), and another user plays music 24/7 (the gyms that have been mentioned before), why should the per-play fee be the same in both cases? If this was a pay-per-play model that would be fine, but this is all-you-can-eat streaming. Users that listen to a disproportionately high number of songs should not dictate which artists get money. That awards those users far more than their normal $10/mo purchasing power.
This scheme is similar to the proposal to calculate artist pay independently for each user, but I think it's a little simpler, since you still only calculate the artist pay out of the global pot, you're just weighing each play by the user's total monthly plays. And you can put a minimum on it too, so the per-play weighting doesn't take effect until the user listens to more than a given number of tracks per month (this way the user who has a subscription but just occasionally listens to a song here and there isn't paying the artist $1 per play, which is to say, until you reach a certain point, listening to other songs won't "devalue" your previous tracks).
This scheme is similar to the proposal to calculate artist pay independently for each user, but I think it's a little simpler, since you still only calculate the artist pay out of the global pot, you're just weighing each play by the user's total monthly plays. And you can put a minimum on it too, so the per-play weighting doesn't take effect until the user listens to more than a given number of tracks per month (this way the user who has a subscription but just occasionally listens to a song here and there isn't paying the artist $1 per play, which is to say, until you reach a certain point, listening to other songs won't "devalue" your previous tracks).