I have to disagree about this part. Ever since his birth, it has been said that Diana was worried about Harry's status as the spare, and she did everything she could to help him carry this burden and not feel left out. The Royal family's worries about Harry were compounded after her death (mainly Charles, William, The Queen, and Prince Philip). Hence their indulgence during his trouble years (Fights with paparazzi when exiting clubs, the heavy partying, the drinking, the marijuana episode et al). It is well known that Harry along with lady Zara Chatto are the favorite grandchildren of the queen. This is why I believe there has been this leniency ever since the engagement. Meghan at Sandringham for xmas, Meghan partaking in official events before being officially married. All of this happened because it is about Harry. If Harry accepts a Dukedom for his wedding, in due time special LPs will be issued for his children to make them HRHs and Princes/Princesses of the UK. After all they will be grandchildren in the male line of a monarch. HRHs and Princes/Princesses of the UK does not only mean working royal, but it is also a matter status. Not giving his children this status would defeat everything Diana worked for to insure the status of spare not be a burden for Harry, by pointing out the difference between him and William (though there is indeed a difference). The only way i think his children won't be HRHs is if he himself refuses. He won't be deprived of it from a top down decision imposed on him, but only time will tell