I agree with you that we should not pay money for this issue, but compare with the hassles and inconvenience, buying a new cable might just be the easiest/fastest way before Apple release a new version of iOS (I personal tested, until 13.3, issue still exist)
my old cable is not even a MFI cable. It’s an authentic lighting cable
before I use the New cable, I tried to upgrades iPhone 11 Pro Max to iOS 13.3 beta, and the issue still exist, I tried reboot both CarPlay and phone servers times, the issue still there: the CarPlay is extremely lagging, the refresh rate is like 2 FPS, the input lap is about 10 seconds.
the tricky part is: I have been using the Apple authentic light cable which coming from iPhone X box all along, works perfectly with my iPhone X, XS MAX, 11 as of today. But does not works with 11 pro max.
since using a new cable from AirPods 2 (still a USB A to lighting) solved the issue, I assume that Apple has upgraded their chip set OR code in recent manufactured usb A to lighting cable, which 11 pro max can only works with the new cable