They could but AM signals have a much larger range compared to FM. FM is mostly line-of-sight - AM signals aren't because they get bounced off the upper atmosphere back to the ground.
AM signal travels much farther and you, technically, don't need local power to listen to it. In cars the latter isn't really true though. If those aspects are the concern it would seem to make more sense to give everyone one emergency set rather than require every car to implement it.
Because AM is frustratingly simple.
FM is a 90-year old technology. You can't expect the government to be at the cutting edge of things.
You can build an AM radio out of 4 resistors, 3 capacitors, a couple transistors that are present in most electronics and easily cut out, and a coil of wire. If you have a crystal, you might not even need a voltage source!
I just looked it up, and there are FM circuits with similar component counts, so I guess I have no idea what I'm talking about! :)