Your first question is certainly a valid question and one that has been on my mind since the start. I'll come back to it in a minute.
I hooked up a BluRay player last night and it worked beautifully for about an hour. I also hooked my laptop up via HDMI and played a few 4K YouTube videos. I had a thought that maybe 1080p+ videos were making the control unit (assuming it's a small embedded device) work too hard, and it was overheating which manifested in the flickers and audio issues. Not sure I thoroughly debunked it with my tests, but didn't prove it either.
Back to Chromecast. Yes, it could be that the Chromecast just isn't compatible with this GM system. My argument then becomes, "Ok, suppose you purchased a $2k television and your Chromecast doesn't work. Would you be upset and want the TV either fixed or exchanged?" My answer is yes. These screens are a $2k option that relies on external components for video playback. There's no onboard disc player and there are numerous references to "streaming sticks" in the marketing. It should work.
That said, I bought Xiaomi Mi Box S last night, which has "chromecast builtin" and I'm probably going to pick up a Firestick tonight. If I can successfully cast YouTube and Disney+ to either of those devices without issue, I'm going to be happy enough to let it go and not pursue a fix with the dealer. Not worth the hassle.