That's really odd. As far as I know carplay just sends video data to the screen and the screen shows it. It's like an hdmi cable in that regard. I would say it's a problem with your car, then. My volkswagen has absolutely no issues with carplay.
[it] just sends video data to the screen and the screen shows it. It's like an hdmi cable in that regard
Spoken by someone who's never had to troubleshoot HDCP handshake issues with hdmi cables.