Regardless of the legal status of the children's titles in the UK, I can't see the point of calling them "Prince" and "Princess" in America, where those titles are not recognized.
From my observations, royal titles - especially British royal titles - continue to enjoy glamor and prestige on a social level in the United States, even though they have no legal effects. The Duke and Duchess of Sussex's own popularity and prominence are evidence of that. If, in adulthood, Prince Archie and Princess Lilibet follow their parents' examples and make use of their royal titles to promote themselves or their ventures, it would likely be very advantageous and profitable.
On the British side, the Sussex children bearing royal titles will probably not make much of a difference during the current reign, but any scandals or negativity that might attach to Prince Archie and Princess Lilibet when they are adults (for adults raised in America with little to no exposure to British culture and the British monarchy, by parents who have expressed prejudices against the country, it would not be surprising if at some point their actions would clash with British values or British expectations of their royal family) will be seen as reflecting on the monarchy of King William and King George to a much greater extent than if they had continued to be called Archie and Lilibet Mountbatten-Windsor. There is a clear difference between the public perceptions of the influence-peddling expose against Prince Michael and his business partner or the accusations of racism against Princess Michael compared to the scandals of the late Earl of Harewood and Gerald Lascelles, who like Prince Michael were non-working-royal grandchildren of a monarch, but unlike him did not enjoy royal titles.
The Letter Patent issued in 2012 for the children of Prince William reflected the change to absolute primogeniture rather than male primogeniture. It stated that all the children born to the eldest child of the Prince of Wales (then Charles) would enjoy a princely title and style, not just the eldest son.
The 2012 letters patent reflect male(-preference) primogeniture as they confer the titles of Princess or Prince and HRH on all the children of the eldest
son of the Prince of Wales. If Charlotte were the firstborn child, she would be the future Queen, but under the 2012 letters patent it would still be George's children, not hers, who would be Prince and Princess.
https://www.thegazette.co.uk/London/issue/60384/page/213
why? No matter what Charles did he was goig to get flak from the Sussexes. if he took away the titles he would be accused of being raicst. If he leaves them, for soem reason he is also bad. what difference does it make if there are 2 kids in the US with princely titles? THey are not getting paid by the British tax payer.
I'm afraid I don't understand your question.
They're in the same position - grandchildren of a monarch, children of a younger son. So for that matter are the Kents and Gloucesters. If a change is made retrospective so as to affect Archie and Lilibet, it'll affect them too. I don't think anyone's going to have their titles removed now: it'd just look too mean. A decision should have been made sooner.
I suppose a retrospective change can be made regarding King Charles' own line and no one else. But it would look too mean.
If King Charles were hypothetically to follow through on his reported original wishes, it would be logical to apply the change to his own reign, and that would avoid removing royal titles from adults who have effectively used them as their names all of their lives.
I do not think the timing of the now hypothetical denial of royal titles has anything to do with it being deemed "mean", since accusations were also made about the denial of a Prince title to Archie during the reign of Elizabeth II, and that was decided long before his birth.
