Historically Cable and (cell) Phones have been slow to recover after major disasters. They may be good enough for warnings, but if after the disaster you need to know where to go to get food, water, or evacuation support you will likely be out of luck.
Broadcast is a little better, but as you go up the technology scale it gets harder to use in a post disaster situation. If you don’t have power we can assume TV is not an option at all. FM is probably using your car, or a pre-prepared disaster radio. AM is an interesting option because you can use an amplified system, or you can use an unamplified system. Simple AM receivers can be passively powered by the signals they capture. It’s not going to be a good loud signal but they can work. If you know what to do, building a simple crystal radio is fairly easy from scrap.
And as @David_Guilbeaul pointed out the transmitter side for AM is also easier to roll out.
