iPhone 13 Pro, things are mostly back to normal on this issue after updating to 16.3.1. I had given up and in December was able to get wifi to my rv I'm living in. It actually was luxurious to use my Apple TV again, as well as have full-time wifi for my laptop without having to hotspot the phone for that. After reading these recent posts, I disconnected my Apple Tv box and hooked up the phone again using the HDMI adapter and cellular data, just to test.
Happy to report that Hulu, HBOmax, Netflix, Disney+ are all back in business. Still a bit glitchy...for instance when I switched from Netflix to Hulu, I had video but no sound. So I unplugged the adapter, closed the app, plugged it back in, and then restarted the app. All good. If things aren't working, try plugging in the adapter and then opening the app. For other apps, try starting the app/program on your phone and then plug in to the adapter. I was able to get all my apps streaming with sound and video, just with a bit of glitchiness as described. But to be fair, before the ios 16 update, I had similar glitchness. So things seem to be back to 'normal.'
When I take my rv up to my property for the summer again where I don't have wifi but have great cell service, it's good to know I'll be able to stream once again, or when traveling.
I guess the notion that this was done on behalf of the carriers to prevent using unlimited cellular data to stream via the cable was not correct after all. Though it sure seemed like it.