In Shakespeare’s King Lear (Act 1 Scene 1), the King divides his kingdom among two of his three daughters. He speaks to them and their husbands and informs them of his wishes as he is aging: “Only shall we retain the name, and all the additions to a king; the sway, revenue, execution of the rest, beloved sons, be yours; which to confirm, this coronet part between you.” In other words, a king is only a king in name, but the monarchy and all of its trappings is truly represented by the crown. And a crown requires a coronation.
While a dictator may rule over or control many people, an absolute monarch possesses both unlimited power and a sense of being beholden to his kingdom. Coronation ceremonies are solemn and/or religious affairs for precisely this reason. The people and their representatives are welcoming the ruler and his rule.
Chazal teach us that there can be no king without a nation. Even as the monarch was born into the position and virtually guaranteed this status, it is the coronation that makes a king into The King. During the Yimei HaDin we experience Hashem as the King of all Kings. As the piyut describes ushering in a golden era, it ends with what will symbolize utopian society: Vayitnu lecha keter melucha. We will coronate Hashem with the crown of Kingship; we will all opt in to what is and always was, and we can appreciate that The Crown represents a loving and welcome relationship.