Yes you are correct in that it is highly unlikely that the members of the British Royal family will try anything crazy while traveling but look at cases like Saudi Arabia or Nepal where members of the royal family resorted to killings. King Faisal of Saudi Arabia was killed by his nephew Prince Faisali bin Musad and King Birendra of Nepal and most of his family were shot dead at a banquet by none other than the heir to the throne. Security screening may perhaps prevented the killings.

The last Iraqi tyrant ruler Saddam Hussein's older son murdered his father's cook in Egypt! He probably traveled on a diplomatic passport and perhaps carried guns.

Granted that these people did not commit their crimes while traveling IHMO the fact that they are members of a Royal family or travel on diplomatic passports should not exempt them from security screenings.