My car has CarPlay and I've found it to be very disappointing, so much so that mainly I now do as you suggest and simply use the iPhone with a dash mount. I get the audio over Bluetooth, which seems to work well enough - it seems the Bluetooth implementation is older and better debugged.

The car's Bluetooth is satisfactory for taking calls.

Part of the problem is the car's unit, as it's Android and it crashes a lot when it's running CarPlay.