Sorry I should be clearer: I think it actually might be feasible in a high population density area and if everyone uses it, but because of the limited range of bluetooth you really do need a high density of active nodes for it to work reliably.

A messaging system that often takes hours or days to get messages to the receiver is fairly useless and people will continue to prefer centralised systems, so there's a severe chicken-and-egg problem to solve there before anything like this can work

There's no reason a mesh network can't use an internet connection as a transport when it's available. Moreover a P2P capable mesh can even make use of a centralized server in such scenarios. At the end of the day it's "just" a message routing and delivery problem.

When I enable WiFi calling on my phone that doesn't preclude it connecting to a cell tower.