Unless you're paying them directly, you're still not paying the artist. Streaming and piracy don't even come close to the drain that labels put on income flow to artists. Artists made just about $23.40 for every $1000 their songs sold for in 2010, according to TechDirt [2].
I wish the world were as you described. But it's not. SOPA came close to destroying free speech online instead of guaranteeing artists their fair share.
[1]: http://www.bradsucks.net/archives/2007/05/22/where-your-musi... (an indie/marketplace artist's view)
[2]: https://www.techdirt.com/articles/20100712/23482610186.shtml (standard industry view)