There are 3 ways you can go about paying artists.
Way 1 is to say that x% of what you pay goes to the artists and that the streaming service takes the rest, no matter how many songs you play.
This makes no sense; this would cause a Taylor Swift fan that listens to her for hours on end, but also listens to other music sometimes, to pay less to Swift than somebody who just plays one Swift song per month and nothing else.
Way 2 is to pay a set amount per play, but make sure that the amount is low enough that if you play music for 24 hours a day, 7 days a week, the payouts are still less than what you paid for the service.
Most people don't listen to music for that long, so this makes artist payouts unrealistically low.
Way 3, which is what services actually do, is to have a much higher per-play rate and assume that users listen to n songs a month on average.
There will be some users who listen to a lot more, and you will take the loss on them, but by the law of large numbers, you will make an overall profit.
This is predicated on the fact that nobody "cheats" the service and misrepresents how much music they've been listening to. If you fraudulently tell Spotify that you've listened to your own songs 10m times this month, you make a lot of money.