David and Sarah still were grandchildren of a monarch - even though they were born after his death. Their granny was the queen mum who was alive until 2002.
And as others indicated, the queen had only one nephew and one niece by her sister - while she has 8 grandchildren. And this nephew and niece were often invited to 'smaller' family meetings - where the larger royal family was not invited.
By contrast, Charles had 6 nieces and nephews and 5 grandchildren. And nieces and nephews are indeed very different from first cousins once removed. Very few people would put Peter, Zara, Beatrice, Eugenie, Louise and James (his nieces and nephews) in the same group as Charles, Margarita, Samuel and Arthur (his first cousins once removed).
I don't think Louise and James receive that much more attention than Peter and Zara because they are styled as children of a peer and their cousins are not. All four of them are grandchildren of the late queen... so they do receive some attention, but I don't think the difference is in being styled or not.
I'm not sure what you mean by 'the issue'. The style being intended for nephews and nieces of the Sovereign? The intention was that children of a royal princess would have a style - therefore their husbands were offered a peerage (for example, the husband of princess Alexandra was also offered a peerage - but refused). In this case they were intended for grandchildren of the monarch (and in Alexandra's case it would have been for great-grandchildren). They were born children of a royal princess and grandchildren of a monarch - just not the current monarch but the previous one. This is somewhat comparable to the title prince and princess being used for children of a monarch (and male-line grandchildren) - Anne, Andrew and Edward didn't suddenly lose it because their brother became king. It does change their place in the order of precedence, but they remain children of a monarch - and no titles are taken away.