I had some uncertainties about the complete correctness of some of what you wrote, but then I read the linked article. I do question some of what you wrote as, within the world of the play and the musical, lots of people would be received by royalty who do not speak with RP. Indeed, Eliza stands out at the Embassy Ball (or the ambassador's garden party) as speaking differently from anyone there except Higgins. Even Pickering speaks with a set of pronunciations that Higgins is able to trace to four different places. And it's quite possible that Eliza's father will be received by royalty at some point, and probably sooner rather than later.
What perhaps would be correct, if I trust what is written at the link, is that at the time Shaw wrote Pygmalion, RP was spoken by so few people — not even the 2 percent estimated in the linked article who would later come to speak it — as to be virtually unknown as a true accent that one might encounter, even rarely, in real life.