[myowncrapulence]

  Is there a system where trust is not necessary, but can still get things done?

Yes. Check out cjdns (https://en.wikipedia.org/wiki/Cjdns) and Hyperboria (https://hyperboria.net)

An entirely encrypted network of relays where ip addresses themselves are encrypted so no one can snoop traffic.

[qwename]

It seems like users are not anonymous, but this lead me to the concepts of overlay networks[1], darknet[2], and mesh networks[3]. Thanks for that.

[1] https://en.wikipedia.org/wiki/Overlay_network

[2] https://en.wikipedia.org/wiki/Darknet

[3] https://en.wikipedia.org/wiki/Mesh_networking

[egh5oon]

No mention of Tor and its Onion Services?