During the ice storm in the Northeast (Upstate New York, Maine, and parts of Quebec, etc., only POTS was functional immediately after, power was out to my home at the time for 11 days, some for 18 days. Telephone service survived largely because the aerial lines were below all the other utilities such as electrical transmission, local distribution, cable TV, even municipal signaling.
And Verizon maintained service by conscripting generators, chargers, and batteries for the DSLAMs necessary to provide service to the last mile or so. It required also that the Maine National Guard provide fuel for this work. Batteries and chargers came from Massachusetts, which had suffered a similar storm the year before centered on Cape Cod, where the current Maine director of operations worked, having transferred from that region. He knew what was needed.
With this effort many who needed life-sustaining medical equipment were identified, contacted, and served. Emergency services were able to save many lives. And of course trouble reports were made possible. My sister lived in a house about a quarter mile from the main road, and electric service crews missed her for an additional week, not realizing there was a line into the woods. Her telephone service went down with that line. I got a call from her when she was at work, contacted a Central Maine Power executive I knew, and they were on site within an hour. Woops. Wood stoves and artesian well in the breach...
Electric crews came from as far as Hawaii to assist in restoration, Eastern Maine hit the hardest. The upshot is that POTS was a vital service during this event, irreplaceable. Today cell service would rely upon backup power, and that might not last 11 days, and further might not be able to, in any way, be extended to address the need.
POTS was a literal life saver here, but knowing how copper is built, this is indeed a technology that either needs modernization or replacement. ATT should be required to offer existing users similar, replacement service, and perhaps CPUC should require this at no significant change in costs, as these users are not at fault. If wireless service is the answer, it should be required to offer the same level of service, hardened against power outages and natural disasters. Walking away from POTS probably does make sense, if the replacement is of similar reliability and performance. And no, ATT doesn't get to claim that current POTS is in any way less reliable than some substitute, this current diminished reliability is more due to ATT's failing craft and maintenance. I see it in Arizona, and it is not anything but lack of attention. No excuse.