AM transmissions have a far greater range than FM transmissions, up to thousands of miles. This matters in a common emergency scenario, a nuclear bomb blast (or all out nuclear war), when EMPs will take out most electronics. Cars are Faraday cages and their electronics will likely survive an EMP. In this case, an AM radio in a car is likely the last surviving broadcast medium people will have access to.
A fair point, but there's no need to have the antenna connected unless the radio is actively on. It could be on a relay. Many radios would be off during the EMP.
In the event of a nuclear bomb blast or nuclear war, assuming that the plan isn't out and out annihilation, even then, communications infrastructure is going to be a strategic target.
FEMA maintains about 80 AM transmitters in Faraday cages, with backup generators, across the country. Amateur HAMs maintain a lot more, though of lower power.
