ndsipa_pomu parent
I'd consider that ensuring that mobile phones have AM reception would be better as some people don't own a car. Consider the case when you have a music festival and thousands of people are camping away from their car if they have one - almost everyone would have a mobile phone either on them (especially if they're using it to buy drinks) or in their tents.
In this era of SDR radio, I'd be surprised if cell phones don't already have the capability with just a firmware update. I suspect the main reason phones don't allow broadcast radio is to create demand for streaming services.
IIRC AM radio requires an antenna, and even the smallest type is thicker than a phone. Not that I'd complain about thicker phones at this point.
Older phones used to be able to play FM, requiring a headphone cable to be used as an antenna.
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.