I think you're overestimating the resiliency of cellular networks.
After the Katrina hurricane, the FCC mandated that cell sites have at least 8 hours of backup power (which isn't a lot when power can be out for days or weeks), but the industry sued and got the rule replaced with 'self-regulation', with the predictable result:
https://www.vice.com/en/article/dyv9j7/how-big-telecom-kille...
According to the latest report by the FCC, about 28.1 percent of the cell sites in the area impacted by Ida are offline, leaving hundreds of thousands of customers without service. Another 354,699 residents in Louisiana, Mississippi, and Alabama remain without landline phone, cable, or broadband service.
https://www.theadvertiser.com/story/news/2021/08/31/cell-ser...
The FCC report shows that as of 11 a.m. Monday, 52% of 2,759 cellular sites across 31 Louisiana parishes were offline as a result of Hurricane Ida. The majority of the downed towers — nearly 65% — were offline due to a lack of power, a problem that could persist for weeks in some parts of the state. In some cases, cell sites are down due to multiple issues, such as power outages, damage to the network or damage to the site itself.
CoWs can help in a small disaster or providing service at a shelter, but when thousands of cell sites are offline, there's still going to be a lot of people cut off from communication.