>Each and every user runs their own instance of a federated server.
That's not federation. Federation is a distinct concept from decentralization; federation does involves trusting a third party of your choice (namely, whoever's running the instance you joined), but simply offers choice of which third-party you choose to trust.
The "everyone can run their own server" thing is just a side-effect of federation not blessing anyone with any sort of exclusivity over power to be a third-party.
Outside of tech circles, your idea is DOA because nobody wants to run their own server just to use facebook. Plenty of people don't even know what a server is, and had the ISP set up their router (and BTW they don't know what a router is either). With federation, you can still have a fairly normal app and get most of the benefits of centralization.
The point of federation is to avoid giving anyone absolute power over the community without recourse, not to completely avoid trusting anyone whatsoever.