Amazon has taken a stab at this with a watch party on Twitch. I imagine you could have a private stream and do it that way maybe? Not ideal of course. It's intended for a different use case.
The best options I've seen involve using sites of questionable legality plus Discord.
Your observations of skew are kind of interesting and larger than I would've expected. But I guess this is the video players being built to show you the content not showing you the content at the same time as someone else. Specifically this means no effort is made to "catch up" in case of buffering. You or your GF must have a lot of buffering. This alone surprises me because Netflix's core delivery tech seems to be extremely good. But again, their delivery tech probably isn't built to solve this problem.
Anyway, while that's an unsolved problem it's not core to Netflix's business and that's the key criteria here.
Video should always be kept in sync with audio and not the other way around. You can freely drop or repeat video frames (within the boundaries of reason) without anyone being able to detect it in a blind test, but audio should not be messed with. This is why when syncing audio and video from different sources during production, the master clock is always the audio.
I can imagine part of Target/Walmart business to be like Amazon so they sell their tech to smaller or local players because they would have loads of knowledge in that specific area of ordering and fulfillment.
It is not counter argument as such - but idea that they could become Amazon competitors in some areas and be tech companies.
They're still solving some interesting problems like how to watch the same content, in sync, with your friends. Interestingly my gf and I noticed that when we watched NFLX together using a video call to see eachother's faces/commentary our video would skew by noticeable amounts across the span of a movie. (eg even a 0.5% speed difference would give a 3 second skew in 10 minutes, which is enough for one to see someone's reaction to a surprising part of the video differ from your own.
So there are still technical fringes to solve that can value differentiate from late adopters like the channel specific providers like say the ABC app https://abc.com/apps