Phones are great for emergency notifications but I think AM would be better for long-term sustained emergencies. It's a highly highly unlikely event though.

Today is day 6 of some people still not having power after the recent barrage of nearly hurricane-strength storms along the southern US.

Those cheap AM/FM/weather radios that run off AA batteries are invaluable.

Phones require cell towers, internet backhauls, data centers, satellites, and power. I agree that phones are an absolutely fantastic first-line platform for emergency notifications. You still need more, though. There are many emergency scenarios that can hamper or disable cellular communication. Emergency preparedness is all about having redundancy and contingency plans. AM radio is extremely primitive, meaning it's low power, easy to run, and easy to repair. It's a fantastic option for a backup emergency warning system. Most people have one AM radio nowadays, and that's in their car. I think keeping that option around is a good idea, considering how cheap AM radio components are.

EDIT: I'll add that I'm fairly progressive. I just believe in defense-in-depth. Information is really important during emergencies, and we should have many ways to warn people that they're in danger.