Apple Watch cannot pair with car audio via Bluetooth

I have been caught in my car a few times without my iPhone. I don't always have my iPhone with me. That's why I have an Apple Watch with cellular service. Anyway, I knew my car audio has a headset feature. I can connect my iPhone using bluetooth and use it like a headset or I can connect via CarPlay. So I figured, since my watch has bluetooth I might be able to pair it. The watch identifies my car as something to pair with, compares PINs and then nothing. Apparently, this is not allowed. But, it gives you every indication that it is attempting to connect. I did attempt to connect to some other bluetooth device and it said not compatible, however I didn't get this from attempting to pair this. Why shouldn't this work? Is this an intentional incompatibility?