If I've been following the whole Ethereum thing correctly, as an outsider who kind of looks down on it, this is right up it's alley. You write some sort of smart contract which allows for the uploading and downloading of music blobs, charges for the service, and if insufficient coins are garnered for storage deletes the least used files.
I don't think you need a server or any such thing, and the only way to force a take down would be to take down the underlying services.
What's to stop the MPAA/RIAA and ISPs from just suing everyone on the network who's hosting part of the file? If they can sue bittorrent users, what's the significant legal difference here?
It's like if someone started a point-to-point delivery business where they take anonymous, secure packages between different places, no questions asked, and then are surprised when the police show up and say they're pretty sure that a good portion of the packages they've been carrying are drugs and pipe bombs, and ask them to roll on their clients, or at least stop delivering packages. And then the delivery man tries to make a philosophical argument that they aren't morally or legally responsible for the contents of their packages, and in any case it really shouldn't be illegal to distribute drugs or pipe bombs.
If you are building a piracy service a blockchain just complicates things and adds no value.
A pretty good rule of thumb is that if you can replace block chain with a database or anything else and lose no functionality, not to mention remove the whole thing together and simplify your solution it's not block chain but bullshit.
Spotify doesn't have the music I want to listen to.