I think this has to do with the origins of the Dutch Republic for starters. During the early years of the Revolt the States-General ditched the Spanish king and actively searched for a new one. But in the end that failed, so they declared sovereignty themselves and made the States-General sovereign while the Princes of Orange became stadholder, an old position as steward, but basically commander-in-chief during those days.

During the Republic there was a big political fight between Orangists and Statists, who respectively wanted more power for the House of Orange or the States-General. This even led to some stadholderless periods in the 18th century. In the latter half of that century, the stadholdership became hereditary and the Prince of Orange became stadholder of (basically) every province of the Republic. At the end of the 18th century, patriots, inspired by the Enlightenment, rose up and with some help of the French, kicked out the stadholder and declared an unitary republic, the Batavian Republic.

Quick jump to 1813, when the French left the Netherlands and the Allies declare the nation independent again. The son of the last stadholder, who fled to Germany, wants to rule his old “domain”, and gets named to be the “sovereign monarch”. The Dutch people, which had a French monarch during the days of the client state Kingdom of Holland, basically accepted it and during the Concert of Vienna, Sovereign Prince Willem became King Willem I of the United Kingdom of the Netherlands, which included both the old Republic and the old Habsburg (Southern) Netherlands.

Sources: Blom, History of the Netherlands Israel, Dutch Republic