There were two kingdoms in the Old Testament era as well, even if they sometimes got a bit blurred, as they did under Moses. Uzziah provides a poignant example of the distinction:
2 Chronicles 26:16-21The point is that the king - the civil head of the country was not the high priest, the religious head of the country. Rather, there was a distinction between the two kingdoms.
But when he was strong, his heart was lifted up to his destruction: for he transgressed against the Lord his God, and went into the temple of the Lord to burn incense upon the altar of incense. And Azariah the priest went in after him, and with him fourscore priests of the Lord, that were valiant men: and they withstood Uzziah the king, and said unto him, It appertaineth not unto thee, Uzziah, to burn incense unto the Lord, but to the priests the sons of Aaron, that are consecrated to burn incense: go out of the sanctuary; for thou hast trespassed; neither shall it be for thine honour from the Lord God.
Then Uzziah was wroth, and had a censer in his hand to burn incense: and while he was wroth with the priests, the leprosy even rose up in his forehead before the priests in the house of the Lord, from beside the incense altar. And Azariah the chief priest, and all the priests, looked upon him, and, behold, he was leprous in his forehead, and they thrust him out from thence; yea, himself hasted also to go out, because the Lord had smitten him. And Uzziah the king was a leper unto the day of his death, and dwelt in a several house, being a leper; for he was cut off from the house of the Lord: and Jotham his son was over the king's house, judging the people of the land.
Under the new covenant, we are a nation of priests. We have direct access to God through prayer in the name of Jesus Christ, and consequently we have no use either for priests or for incense. We do not need a merely human mediator, because Jesus Christ, the God-man, is our mediator and high priest, and the Spirit communicates on our behalf.
The passage is also a good reminder of the second commandment, the commandment that teaches us that God must be worshiped as He wills, not as we will. Here, Uzziah was not proposing to offer incense to Baal or to any false God, but rather to YHWH. Nevertheless, he overstepped his bounds and did not follow the way of worship that God had appointed, and so God judged with leprosy.