An FM/AM antenna is a wireless receiver. Not a transceiver (though CB is and is still common in long-haul trucking), but still, it's always been possible for someone to hijack the channel and send an unwanted signal into your speakers. That's how pirate radio worked for a century. If all an attacker can do is send sound into your cabin, that isn't a meaningful vulnerability. They could do that with a megaphone.
If car makers are actually hooking the bluetooth chip up to anything except the sound system, that's the problem. Although, assuming a class 2 device, it only has a 10 meter range. If an attacker is that close and wants to shut down your car, they can use a nail strip.
The real problem here is hooking up WWAN to control software.
The trouble is, the sound system is inevitably connected to the rest of the car. For example, in most cars the volume automatically increases with vehicle speed to compensate for increased road noise.
These connections could be physically 'one-way' but in practice most modules are simply wired in parallel on a CAN bus and something like the radio would be set up to
send data to the car's CAN bus (for diagnostic purposes at least).
More than just speed sensitive volume now. Replacing the stereo in my van requires a conversion box (Maestro) that deals with the various car settings that are done through the stereo, such as dome lights out duration, dash clock setting, auto door locking, etc.
The stereo is way too tightly coupled with the rest of the vehicle.
If car makers are actually hooking the bluetooth chip up to anything except the sound system, that's the problem. Although, assuming a class 2 device, it only has a 10 meter range. If an attacker is that close and wants to shut down your car, they can use a nail strip.
The real problem here is hooking up WWAN to control software.