P2p mesh is great except there's no DNS, so now either someone needs to host that, making them a critical node. Either that or every needs to start memorizing IP addresses. Using discovery through broadcast would easily create so much traffic that you'd run out of bandwidth on a wireless mesh.
Everyone seems to think that a wireless mesh is some kind of golden bullet, but it's really not. Putting that many people on a mesh generates a lot of broadcasts, which by nature go to everyone on the net. Having broadcasts rebroadcast by mesh stations will double the traffic load each time it's done, so beyond 4-5 mesh points, and a few dozen clients, the broadcasts start to take over the available bandwidth.
Rebuilding, basically means that someone needs to set up an IX, and connect their neighbors to them in an ISP-like configuration. One person basically needs to become the ISP/IX for a neighborhood and connect to others doing the same for their neighborhood.
At least one of the IX owners would need to know enough about networking to set up routing protocols and run an IP address management system to ensure nobody overlaps anyone else, and configure routing protocols for all the IX locations so they can communicate to eachother.
Then there's the problem of services. The global DNS system is down, so you need to make a new one. Services you expect on the internet are gone, so those need to be rebuilt, which means someone needs to basically become a datacenter to run the servers to generate those services.
I would be the obvious candidate to do this in my area. I know of a handful of people who could do the same in their area, and only one such person lives remotely close to me (about an hour or so drive away). I have my own homelab servers, and more networking equipment than I can shake my fist at. I'd go and raid the local ISP distribution building to pillage some fiber delivery equipment and build out a gigabit+ speed passive optical network from my basement as the ISP/IX/DC.
Finding outdoor rated fiber lines and whatnot to run any relevant connections would be important.
Then set up a wireless point to point link to any other nearby community networks.