There is no fear that a modern king will attempt to override the constitution: it is more likely that he will ignore the constitution and work behind its back. He will take no advantage of his kingly power: it is more likely that he will take advantage of his kingly powerlessness— of the fact that he is free from criticism and publicity.When Chesterton wrote those lines in 1908, it was probably quite true of His Majesty King Edward VII. Even almost 30 years later, during the Abdication Crisis, the British public knew very little about what was happening, unlike the American people, in whose newspapers it was headline news.
However, mores change. With the advent of television and the accession to the Throne of a beautiful, young Queen, the Monarch became 'newsworthy'. Still, there was very little criticism when I was a boy.
But, today Her Majesty and the entire immediate Royal Family are undoubtedly amongst the most criticised and public people in Britain. The biggest change probably began with the marriage of Charles, Prince of Wales to the Lady Diana Spencer, 'Lady Di'. The romance of the Heir to the Throne marrying a beautiful young woman in a ceremony televised worldwide, put the Royal Family in the spotlight. They continued there through the problems in the marriage and the problems of the Duke of York and his wife Sarah, with both marriages ending in well publicised divorces.
The marriage of the Duke of Cambridge to miss Middleton and the birth of their (now) three children have kept the family squarely in the public eye. The upcoming Marriage of Prince Harry of Wales (I wonder what Dukedom his Grandmother will give him?) has generated even more publicity and intense criticism, ranging from 'How can he marry a divorcée?', to the racist cries of 'But she's not white!' (As an aside, His Royal Highness is descended in part from a Mongol Khan, so I guess he's not 'white' either!)
At any rate, Chesterton obviously did not foresee the development of the modern media and its effect on the privacy of the Royal Family.