AM radio does require an antenna of some description, but usually the signal received through even a tiny bit of metal will be more than sufficient. The problem is usually dealing with locally produced noise (e.g. someone using a microwave or switching lights on and off) rather than trying to pick up a weak signal.
For the purpose of emergency broadcasts, maybe using both AM and FM would make sense.
Older phones used to be able to play FM, requiring a headphone cable to be used as an antenna.