Again, it is your opinion that he does not want to change, and that he needs to change. Do you know the intimate day to day details of his work day? I am sure that you have an understanding through your research, but I doubt seriously that the palace gave you carte blanche to all of the inner workings.
What's wrong with IOC candidacy/membership? It promotes Denmark to the world. A great many of the royals are or were members of the IOC, inluding currently: Princess Nora of Liechtenstein, Prince Albert of Monaco, Princess Anne of Great Britian, Sheikh Ahmad Al-Fahad of Kuwait, The Grand Duke of Luxembourg, Prince Willem Alexander of The Netherlands, Raja Randir of India, Prince Nawaf Faisal of Saudi Arabia, Sheikh Tamim bin Hamad of Qatar, Prince Tunkuy of Malaysia, Princess Haya of the UAE, to name a few, and I would consider these his compatriots.
You can't have it both ways, either you can have a monarchy with all of the trappings of tradition, or no monarchy at all. A monarchy is by it's very definition different from the majority of the population of a country. They are there to represent the country on an international stage, and to do so with as much grace and dignity as the position entails. So you can't therefore compare them to the majority of the population. Would the majority of thepopulation have the journalists and papparazzi following them constantly? Have every move and every word dissected? Have every single moment of your life made public? No. Nor would the majority of them choose to live such a life. Unfortunately or fortunately, Frederik had no say so in who he was born or what he is destined to have to do. He couldn't have just said, well, I don't want to be king, I'm going to be a soldier, banker, candlestick maker. We all have that choice. He does not.
You can't know for a fact what the job entails as you are no royal, just like I can't know what it entails. However, I am more than willing to give them more credit becuase I can't imagine the pressures that come with such a position. I honestly think that they do more than you give them credit for.