Well, they can archive the profile too then I'm assuming. So you can't really ever kill the fact that entity existed in such a scenario, but you can stop using it from its original space. It seems to me that companies like PDL and Oxy, (even the smaller players like RapLeaf potentially), could still put together your identity since they use the full body of your internet usage, and even non internet information about you.
I know it's hard to thwart people like Oxy, that are stacking all sides. Providing both VPN and proxy services. Then using those services to sell anonymized scraping as a service. Then collating online data obtained from scraping with offline data to create ridiculously detailed profiles about people. (Then leaking them all by the way. As though collecting them wasn't bad enough. [1]) But my ideal distributed social media would be architected to defeat something like Oxy. Because Oxy, PDL etc are already behemoths and the government has more comprehensive data on you than even Oxy.
I realize though that aether is probably just something to "keep the honest people out" so to speak. But my vote for a "nice to have" would be the ability to thwart some of the data mining and linking baddies that are out there.
[1] https://news.ycombinator.com/item?id=21606415