Why assume that you have to charge every user the same amount and then divide up the income fractionally based on usage? An (arguably simpler) alternative is you begin by paying a fixed constant amount to the artist for every stream, then figure out a pricing model.

I'd also argue that "fairness" is not really that important. One could in theory charge a fixed monthly rate to customers and pay a fixed constant fee to artists as long as the company's finances work out favorably. It's not really the customer's business how the company's costs are distributed.