Why would you want to exchange private messages with anonymous counterparties?

- You participate in a secret cabal, and don't want participants' identities be visible to each other.

- You're a journalist, and want to give your informants in sensitive matters, or from oppressed countries, a way to securely interact with you, so that you won't be technically capable of reporting their identities.

- You're selling illegal goods or services.

I'd say that in the first two cases I would consider running a separate copy of the network, because it apparently involves one supernode, and I might want to control the supernode (or maybe not).