I mean if your radio is off then it won't play, right? Always works for me. Your device won't initiate your car's radio if it's off.Apple must have implemented the simple mode in order for the car to switch over to it in the first place. All I'd like is an option to disable it when I have a passenger.
You could also turn off the music app. Generally if it's not running in the background, CarPlay won't pick it up automatically.