But the rules can be changed. As I stated they aren't written in stone. For example, the Queen issued Letters Patent ("changed the rules") in order to allow George and Charlotte to be HRHs and not HHs.
If rules can't be changed we wouldn't be discussing titles for Harry or William's children in the first place. We'd be discussing titles for the children of the Hereditary Princess of Liechtenstein. Because if rules can't be changed the Act of Settlement would never have been passed.
George V banned HH in the UK in 1917 when he issued the LPs that cover who is and who isn't an HRH. Under those same LPs George would have been HRH anyway.
Under George V's LPs the following were/are automatic HRHs:
Elizabeth, Margaret, Edward, Alexandra, Michael, William, Richard (his male line grandchildren - his own children had been raised to HRHs by Queen Victoria in 1898)
Andrew, Edward - born as the children of the monarch
William, Harry, Beatrice, Eugenie, Louise, James - male-line grandchildren of the Elizabeth II through her sons.
George - the eldest son of the eldest son of the Prince of Wales.
Spouses of the men listed above - Katherine, Marie-Christine, Birgitte, Sarah, Sophie, Kate and Diana and Camilla.
Yes I have
a) left out Charles and Anne
b) included Louise and James
c) left out Charlotte and the new baby
a) special LPs were needed in 1948 to give HRH to Charles and Anne when George VI issued the LPs to give the right to HRH from birth to the children of The Princess Elizabeth (without those LPs Charles would have been born as Lord Charles Mountbatten, Earl of Merioneth - he would have been able to use Philip's second title as a courtesy) and Anne would have been Lady Anne Mountbatten.
b) The Queen didn't issue LPs to strip Louise and James of HRH but made Her Will known - which has the same effect (I have confirmed this with BP - wrote a letter asking this very question and was told that they are not and never will be HRH as the Queen's Will was made known). Given the reported 'smaller royal family' idea going around the decision is clear that the children of the younger sons won't be HRHs over time.
c) special LPs were issued to give HRH to all of William's children not just his eldest son. They didn't want a situation to arise where the first child was a girl and born as Lady Charlotte Mountbatten-Windsor and then a son born as HRH Prince George when they were changing the law to allow the girl to be the future Queen.
The rules that have been changed by since 1917 have been done for clear reasons but mainly to ensure a 'future monarch' is born as HRH.