Peer-to-peer means not having a 3rd node sitting in the middle of the communication in some data center. E.g. rather than client->server->client it is just peer->peer.
But I've run across people who think a client-server protocol necessarily isn't peer to peer. I'm just trying to argue that the p2p protocols are still client-server protocols. Nostr could be written as a p2p application without changing any of the NIPs, just by making every client also a relay.
Your point is the part I didn't discuss because it wasn't in my head at the time --- the middleman. You want direct communication over anything with no middleman. Fair enough. And I think that should be achievable, even if the communicating pieces are a client and a server.
