I did a bit of research, and there was a coin from 2014 that tried to do something similar (VPNCoin, VASH), but it looks like the development is pretty much dead.

As for running an exit node, I'd assume (layman speculation) that they would have to make sure that an exit node cannot see what they are letting out of the network. So, probably encryption always, and possibly the network generates fake requests so an exit node has plausible deniability about who it is communicating with, if that is even relevant.