Proof of work is a great solution for how to give a signal to trust someone that you don’t otherwise have a reason to trust. Bitcoin trusts no one and thus burns the planet.
I like your idea of having a shared Dat once you make a connection with someone.
I wonder though about how many people you’d want to share an encrypted Dat with, though? The scuttlebutt client on my desktop always felt sluggish, in part because I think it was trying to decrypt every message on the planet. I guess that’s another tradeoff: they don’t specify a recipient for private messages to make metadata harvesting about who is talking to whom harder.