The Internet is _not_ for talking to people across the globe. The Internet allows that, but not only that - one can have a Whatsapp chat with someone in the same bus, this is both legal and technically possible.technically possible but rather redundant and in most cases pointless. (yes, there are exceptions)
so i rather strongly disagree. 99% of my use of the internet is to talk to people across the globe. it's its primary use case. the example you mention is a fringe application, useful to a tiny minority.
"the network remains functional during internet outages"
that strongly implies that i can use this app to replace other apps that use the internet. but i can't, because it does not allow long distance communication the way internet based apps do.
so for 99% of my needs this app is not helping me. it does not make me independent of the internet. i have been in places where the internet was cut off due to political turmoil. and i have friends who have that happen to them. in all cases the main challenge was the lack of long distance communication. local communication was barely affected.
sms and phone still worked, and in fact the app that would have helped is one that can route data connections via sms and phone calls. like old acoustic modems.
infrastructure independence at a local level is nice, but much less serious or critical than independence for long distance communication. and long distance already starts at a few km.