Emphatically not. I want the head unit to act as a dumb terminal for the phone. My first instinct would be a USB-C docking station supporting DisplayPort video, various interesting USB devices, and a descriptor that makes it clear it's a car's head unit so the device can intelligently offer a car-specific experience.
Oh, right, more like a car-flavoured docking station? That does sound better, it relies on the car for less in terms of functionality so it should be more consistent and futureproof.