The priests of these temples initially had all the power because they were able to communicate directly with the gods, and that was a useful talent because Mesopotamian gods were moody and frankly pretty mean. Like, according to Gilgamesh, they once got mad at us because we were making too much noise while they were trying to sleep, so they decided to destroy all of humanity with a flood. The Tigris and Euphrates are decent as rivers go, but Mesopotamia is no Indus Valley with its on-schedule flooding and easy irrigation. A lot of slave labor was needed to make the Tigris and Euphrates useful for irrigation. They're also difficult to navigate and flood unpredictably and violently. Violent, unpredictable, and difficult to navigate. Oh, Tigris and Euphrates, how you remind me of my college girlfriend.