But I mean not showing Ancient Arda at all while someone is talking about the three elf-fathers walking around discovering the 5 groups of sleeping elves. I think it would be extremely detrimental to show that. Because it is a story with a 'moral', and not a truth of the universe type of moral at that. [Basically, don't hold out waiting for something better, because it might never come.] If it is Arwen and Celeborn discussing this, Arwen can say that her mother told her the story, and Celeborn can be like, ah, yes, I remember telling her that when she was little. But keep in mind that Celeborn's grandfather was at Cuivienen (in our version, apparently), so to get from eyewitness accounts to nursery story in 2 generations sounds a bit implausible.
I am fine with having unbegotten elves at Cuivienen, and I am fine with them awakening with their partners. I'm also fine with three distinct 'tribes' there, if you will. But we don't want the viewers laughing at them, so I do not want to show the 'let's find the sleeping elves and claim them as our own personal toys' segment on screen.