In the event of a city or country wide black out or similar, then your mesh network still requires someone to be connected to the internet to relay information back and forth to the rest of the network. It's one thing to trust that person to broadcast a transaction for you, but it's another altogether for an entire town or city to be relying on one person's internet connected node to relay all the information through the mesh network. I suppose you could partly mitigate this by also running your own node via Blockstream Satellite.
It is not to be "one person" in charge of connecting the mesh to the rest of the world, multiple paths could exist supported by a smart gateway protocol. I'd suggest such a mesh based approach using mobile devices as a default topology for low bandwidth use cases.