Please note: Adam needed neither one of them, because he was already both of them. Before the fall, Adam was a king with administrative authority over the earthly domain, but was also a priest who enjoyed immediate, direct and open fellowship with the Father God.
Focus Point: Remember that God's original plan was for both king and priest to be the same person, but every since the fall of mankind, this world system has been trying to keep to two separate systems. When God delivered the nation of Israel from the slavery of the Egyptians, He called them to be His own people. This is what He stated to them:
Constitutional Scripture: Exodus 19:5-6 Now therefore, if you will indeed obey My voice and keep My covenant, then you shall be a special treasure to Me above all people; for all the earth is Mine. 6 And you shall be to Me a kingdom of priests and a holy nation.' These are the words which you shall speak to the children of Israel."
Focus Point: God wanted a nation of people set aside for Himself. It was God's desire to bless all nations and people of the earth through Israel, as He had promised Abraham centuries earlier. That is why He called the nation of Israel a "Kingdom of priests". They were to be the representatives before the rest of the world. Although the nation of Israel as a whole failed in this regard. God did not abandon His original plan and design. In the fullness of time, Jesus came not only in the flesh, a son of Israel, but in the Spirit, God's promised blessing in the world.
Please note: From what I have read; God always wanted a priest with a crown.
Please note: The problem with a democracy, republic, monarchy, dictatorship or any other system of human government is that they separate the offices of the king and priest. We call it here in the United States "the separation of church and state".
In a fallen world, it is probably a wise and necessary concession, because with sinful people in charge of the power of the state combined with the power of religion easily becomes overwhelmingly oppressive. Separate offices of king and priest can serve as balances against each other.