Those are great points. Diana's warm gestures were genuine to her nature. That scene where Charles berated her, IMO was meant to show the gulf between those actions and the way the rest of the senior royals behaved. And to show that, at least at that point, Charles really hadn't grasped that Diana wasn't performing a phony "stunt" for the cameras. She had an almost uncanny gift of empathy for people who were suffering in any way.
That kind of behavior probably *would* have been a stunt if Anne or HM or Charles had tried it. I've read that the Queen has a horror of what she calls public "stunts," inauthentic public behavior performed for the benefit of polishing the PR image. There are degrees of it of course, but this series does IMO accurately show that HM is by nature a reserved and somewhat serious person. That's not at odds with the cultural "stiff upper lip" reserve of the British ruling/aristo classes so it's worked pretty well for her as head of state. I suspect that until Diana came along and demonstrated warmer behavior, that reserve displayed by HM was ingrained and ossified as the expected and appropriate royal public behavior, with of course everyone in the BRF taking their cue from the boss at the top. As you put it, "a chilly remove."
I don't snark on Anne for refusing to hug kids just for the benefit of a photo opp; it wasn't authentic for her. She did her bit for her chosen charities, including many non-glam trips to Africa and behind the scenes service on boards, etc. And I think it was an honest response that respected the kids she didn't want to hug for the cameras. I hate the assumption that any random child would welcome a hug from a stranger. I assume that Diana could read the room, and didn't force her hugs on kids who didn't want them. If any of those kids who were present when the photogs asked Anne to hug one of them, understood what the photos were asking, they might have been rather relieved not to be grabbed for such an embrace by a stranger. Sheesh. Those kids were people, not props.
Yes, I believe that over time, the BRF learned lessons from Diana's style of public appearances. But in the maelstrom of the first decade of Diana's marriage, I doubt that any of the senior royals understood that her warmth was as genuine as their public reticence, and they were increasingly frightened by the implications of the huge public response to her press coverage. That may have been Charles screaming in her face after her NY trip in this show, but IMO it well represented the fears and frustrations of the BRF in reaction to Diana's tsunami of press coverage and public fandom.