There are various mesh-network projects around and it's better than nothing, but their issues tend to be pretty low bandwidth and physically limited area. Wifi-mesh in a somewhat densely populated area is technically possible, but technology says that you need to be pretty close (100m give or take) to the next node. On rural areas people have built pretty long range wireless jumps without ISPs but hardware requirements for those are a bit different and you're relying heavily on the node next to you in upstream direction.

Then there's things like LoRa Networking, but their bandwidth is very small and it's really only suitable for SMS-style messaging with pretty low traffic, but it can reach up to 10km between nodes. AX.25 over amateur radio has range up to hundreds of kilometers, but it's also pretty slow (~1kbps).

So, in practise, the best would be to use something like NNTP and distributed servers across the mesh network where you're less dependent on long range high speed communications. Modern web experience or instant messaging just isn't really feasible over any mesh network with current consumer-grade hardware.