What I think
With that in mind, I feel this concept is very close to a lot of the p2p or decentralized content distribution systems being tested out these days, like aether or matrix.org.
The backend implementation that matrix.org uses is rather ideal. It's Federated JSON over HTTP(S). The clients out today are heavily focused on chat, but it is data agnostic. You could have client that writes rich media content and a client that displays this as a blog. Going back to the streams concept, you could have a client subscribed to multiple streams (rooms in matrix vernacular) and as people post their messages - rich media or simple "how are you" comments, it would get federated out to each home server, which can present a web client interface like in tonsky's mock-ups.
For the concept of amazon providing sensitive order information as a stream/matrix room, there would have to be an add-on concept built into the client of some sort of security token. I'm not talking about a losable gpg keypair, but something amazon generates and provides to you (like they do with their AWS services already) Amazon would then create a personalized stream for you, using that security token to encrypt. Since amazon provides the content and the key, they can replace your key at any time.
And now with Aether - has no one heard of freenet and i2p and Tor? No, we'll re-do all the sort of starting work on anonymity and security and get to re-make for the thousandth time the mistakes where it really isn't that secure or anonymous rather than building on anything that has at least some of the actual battle testing and bug squashing already done.
What is Aether but Frost with less testing? Hell, what is it but TOR access to Usenet? Maybe I don't understand what's so special that it can't use any of the long worked on infrastructure level work that's gone into the above projects for a decade or so, and it actually does make sense to start over from day one - but if so, they certainly don't explain it.
And I'm not talking about UI - I'm talking about the anonymity equivalent of deciding TCP isn't good enough so I'm going to re-invent IPX or something.