I think the thing is that it comes to pretty much the same assuming everyone watches the same amount of music. Let's say there are three listeners, you each play 5 songs and each pay $5. If you listen to only one artist while the other two listen to the pop artist then there are two ways to do the payment:
Your artist gets your money: $5
Your artist gets the division of the total: 5 times played / 15 times total * $15 = $5
Same either way. This breaks down when:
a) Different people play different amounts of music
b) Non-paying people's music plays are included in the division
Your idea of people paying their artist extra would also break that of course.