[x1798DE]

>Is this problem even solvable on a fundamental level?

I think it is, though it may never be practical. In theory, you could have every node everywhere constantly streaming encrypted noise to every other node, and when you actually want to communicate something, you just switch out the noise for something you actually care about. You'd never know who is actually talking and who is just sending noise.

As you can imagine, that would take a lot of bandwidth and probably a lot of computing power, but it would have very high latency.

EDIT: To clarify, I mean nodes on the network, not relay nodes. Potentially you could use a relay system, but that wouldn't be necessary if everything on the network was constantly in connection with everything else on the network.