It actually does exist already, in the form of Secure Scuttlebutt (
https://en.wikipedia.org/wiki/Secure_Scuttlebutt). Friends connect directly to each other. When you want to get news about someone, you download from them directly, along with news from friends of friends. If both peers aren't connected at the same time it is possible to use pubs, which are kind of hubs accepting all content and distributing to whomever wants it. Pubs have no special functions apart from being a store-and-forward, so you're not associated to a pub in particular (you can be on multiple, or none at all) and no pub is more "important" than others. Nothing is lost when a pub closes.
Cryptography makes sure that only the intended reader can read (unless it's a public message), and that messages can't be forged.
The nice things is that it's all just a message passing infrastructure, and applications can and have been built on top of it, like a git repository system or a music sharing application. So, yeah, it is feasible.