Couldn't God just work through an exalted human agent? Why must the mediator be God?

The pattern you are leaning on is real, God does work through Moses and the priests and the prophets and the kings, and the agency reading is ancient and coherent, held by serious people, not a foolish position. And you are right to want the line drawn from the text, not from a creed.

But this covenant's mediator does not merely represent. He does the work. Moses conveyed terms and sprinkled the blood of animals, and that covenant broke. Joshua at Shechem, Jehoiada for Joash, Josiah after the scroll, every one of them renewed a covenant, and not one poured out the Spirit of God, wrote Torah on a human heart, or forgave a sin. That is the ceiling of a human agent. The new covenant's mediator walks straight through it: He pours out the Ruach (Acts 2:33), He forgives sin on His own authority, and the room asks exactly the right question, "who can forgive sins but God alone?" (Mark 2:7). And monotheism seals it: only YHWH gives His own Spirit, "I will pour out My Spirit" (Joel 2:28), "besides Me there is no savior" (Isaiah 43:11). A creature cannot put God's own breath inside a person. So the One who does it is not an agent sent by God. He is God, doing it Himself.

Do not take it from me. Read Joel 2:28, where YHWH pours out His Spirit, then Acts 2:33, where Yeshua (Jesus) does it, and ask whether an appointed agent could perform the act the prophet keeps for the LORD alone.