For starters, FM broadcasting is hardly more complex than AM broadcasting and any vehicle built in the last 50 years with an AM radio also has an FM radio.
I can't imagine a scenario where FM broadcasting is somehow unavailable, but AM is. But further, if AM is the last line of communication, we are in a VERY bad situation indeed, like apocalyptic. One in which I doubt any survivors are listening to the radio in their cars.
But even further, in an emergency, it's highly likely that car drivers aren't even listening to the radio. Like, unless it's something that everyone is made aware of with communications other than through AM radio. But if those lines are open, then why wouldn't communication be broadcast through those lines?
You may as well argue that we should make sure all homes have land lines or telegraph lines. After all, that's also a line of communication that could be used in an emergency.