It is not required to have just "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.
Sure, but what is the likelihood of such a scenario? In such a case where there is a city wide black out, but enough internet coverage via cellular or satellite for multiple connections throughout the city in question, then how necessary is a mesh network? If some people can still get online via cellular or satellite, then surely most people can still get online? And the few who can't are much more likely to simply use someone else's connection or some public hotspot than they are to set up a mesh network. If there was a mesh network already functioning, then sure, but there is pretty much zero incentive for people to set one up or maintain it for some very hypothetical situation in which not trading bitcoin would be the least of your concerns.