So grandchildren of the Monarch in the male line are automatically Prince or Princess? Is there a lawful way to remove those designations, once ‘earned’? Since no public money is expended on children with those titles, why should anyone care?
Or is it just malice toward their parents? At any rate, some consideration of the implications of their places in the line of succession might be justified.
The only ways these styles can be removed is via Letters Patent issued by the monarch or via legislation by parliament.
It is nothing to do with malice towards their parents as this idea has been floating around now for about 30 years, including the idea of stripping the York princesses of the HRH Princess styles and is the reason why Edward didn't give his children HRH. He didn't want his children to grow up with it and then have it removed once Charles was King.
What implications are there about their place in the line of succession? Most of the over 5000 in that line don't have HRH including Princess Anne's children and most also don't live in the UK, starting with the King of Norway. In addition most aren't British citizens either.
Currently the only ones in the LoS with British HRHs:
William, George, Charlotte, Louis, Harry, Archie, Lilibet, Andrew, Beatrice, Eugenie, Edward, Louise, James, Richard, Edward, Michael and Alexandra. Alexandra is currently 56th in the LoS so of the first 56 only 17 have HRH and four of them don't use it. The person who is 10th in line has no HRH and isn't eligible for it under the existing rules. When Peter Philips was born he was 5th and didn't have HRH. When the current Earl Snowdon was born he was also born 5th.