Freenet, as a distributed data store, just makes the issue worse. Now I'm expected to host images and videos that other people send. Also a distributed data store doesn't free you from downloading random inboxes either. Someone just needs to to be running enough instances to be able to track and identify you if you're only downloading your inbox.
That's why Tor makes you bounce between multiple nodes, to decrease the chance you get only nodes that belong to a tracker. Actually not sure why I didn't think of Tor as something that already fulfills all those anonymous requirements. It's also an example of the drawbacks of being completely anonymous, that network is extremely slow and will definitely not scale to anything mainstream.
Ie any block could be useful for multiple inboxes and messages. See also how freenet used to do it. https://en.wikipedia.org/wiki/Freenet