Over these last few years, I've come to believe that many of the United States' problems might have been avoided if it was a monarchy (without getting rid of the office of the President, just to be clear). Right now, the most powerful person in that country is, by default, partisan. With how votes are divided, almost half of the country will feel as if the President does not represent them, and they will feel little to no attachment or pride in him/her. The only thing that might bind people together outside of the political party they support is the country itself, which is a nebulous concept that is swiftly losing its importance.
That's why I feel like the monarchy still serves a purpose. Here in Norway, the position of Prime Minister might change based on elections, but there's always, always a person at the very top, even if only ceremonially, that ascends politics and serves as someone everyone in the country can feel pride in. The position of King has little practical value in daily politics, but the value to the national image is vital.