smacw wrote: “It is likely that the Queen chose Cambridge rather than another of the vacant royal Dukedoms because of her grandmother's (Queen Mary) mother (Mary Adelaide of Teck) being the daughter of a Duke of Cambridge who was a son of George III.”

This connection is probably also why Queen Mary’s father, Prince Francis, became Marquess of Cambridge in 1916, having given up his German title Duke of Teck.
Perhaps George V felt unable to make him Duke of Cambridge because Francis was not a British royal, but wanted to keep a link to Mary’s (long deceased) grandfather, Prince Adolphus.
Regards,
Mike