As does our Queen, this is standard in a constitutional monarchy, is it not?
And one who is even more popular is our Crown Prince, he's been in all over the military, including our special forces, and despite being very much a 'man of the people', I doubt that he would ever act against the government when he becomes King, it could very well prove to be the end of the monarchy if it happened.
At least, it almost did in 1920, when Christian X dismissed the government and installed his own, although he later became a national hero for staying home and opposing Nazi rule.