This is how Secure Scuttlebutt works. Scuttlebutt was the inspiration for much of what is nostr. I think we could get to efficient gossip between apps / relays which would help a lot. That said, scuttlebutt started out 100% peer to peer and offline first, and then evolved to have pubs which are like relays. We need relays for the network to function efficiently. But there’s no reason apps can’t be local micro-relays. 

Then you also get cool things like syncing over mesh networks, censorship evasion, and nostr working when the internet goes down or is non-existent.