This demonstrates a real issue: even information you "own" and feel like you can pull the plug on, really becomes part of a global discussion that can only be lessened by removing it.
A tweet you posted 10 years ago might be irrelevant noise to you, but someone else may have quoted it, assuming it's archived on a "too big to fail" platform, effectively eternal, and then from there it spreads into other conversations.
Who's responsible for deciding how and when to archive that?
Aside from that, there's huge historic value in the mundane in the aggregate. We have fine-grained knowledge of the rise and fall of cultural trends and figured-- the sort of stuff that will never make a "formal" historical record but will richly flesh out future understanding of early 21st century life. Much as many of today's historians will get more value out of a Tudor era garbage dump than a perfect statue of Henry VIII, social media will be an unimaginable treasure trove for 2500's historians.
Even if for nothing other than all accounts are banned, eventually.