Good snaps get stored and shared forever, everyone knows to screenshot dumb posts on FB, and there are plenty of twitter archival tools. Youtube's DRM and takedowns work OK against film pirates, but it's still easy to find many movies and redistributed personal content online.
Though I'd be curious what fraction of those instances are someone speaking without thinking, or accidentally sharing to a broader audience... the former seems PEBKAC and the latter is a solvable UX issue.
Even on Hacker News, the various moderation features and things like being able to edit your post after publishing make a difference to how the community works. It's not only what you can get away with but also what people feel like they have a right to do.
An interesting proof of concept might be to try to create a forum like Hacker News, but using distributed software.
Using email, the rule is that if someone sends you something, you own it; they could ask you to do delete it, but you can refuse. Facebook and other social networks let you edit and delete posts. Snapchat became big because you can send pictures that are automatically deleted after you view them.
Sure, you can reimplement basic message exchange in a decentralized way, but figuring out how to enforce the same rules in a decentralized system is nontrivial.