I worry that giving users a "clean up my graph" button is just going to increase the value of user data, since it'll no longer have stale connections or reflected tastes.
That may be true (e.g. Facebook knows my musical tastes as of 12 years ago, which aren't relevant today), but I might be willing to pay that price in exchange for transience. A social network that resisted bulk archiving by third parties, and removed content in a permanent and legally-binding way after a given interval, would be providing a genuinely useful service. When you put something up on the regular web, its lifetime is completely out of your control. Sure, there would be screenshots and individual copying, but such a service could prevent bulk mirroring.