Maybe Twitter is too specialized an example. What about any kind of search? You do need an index, and someone still has to own that index, and “donate” computing power to update that index. You own your self-hosted data, like many of us already do, but there will still be gatekeepers, e.g. Google for our current web.
EDIT: I realized that with a clever enough architecture and probably much more computing power than necessary in a trusted environment, no one needs to own the index. But it seems way more advanced than this protocol. (I’m completely new to this stuff so please excuse my naive skepticism.)