There is not a separate chapter in Cook’s The Social Roots of Biblical Yahwism about the Psalms of Asaph, but I refers to them throughout as part of the Sinai tradition.
I appreciate that he takes a position much like I took when I blogged through the Psalms of Asaph. They come from singing Levites and reflect the Assyrian crisis in Northern Israel. These Asaph psalmists came south where King Hezekiah welcomed them. They edited their collection of Psalms then to fit into use at the Jerusalem Temple.
These songs prefigure Deuteronomy. I have always been struck by how the opening verses of Psalm 78 sound the same theme of passing on the Torah and the Exodus story from generation to generation that you find in Deuteronomy.
Cook says that the editing of these psalms to bring them closer to Zion theology is not totally alien to the original Asaph psalms. He takes Psalm 78:70-72 as part of the original, unedited poem.
“He also chose David his servant,
and took him from the sheepfolds;
from following the ewes that have young,
he brought him forth as the shepherd of Jacob, his people,
and Israel, his inheritance.
So he was their shepherd according to the justice of his heart,
and guided them by the skill of his hands.”
The Asaph psalmists were not against David. They admired him as a humble leader not a tyrannical monarch.
“David leads the covenant people here not as a monarch per se, but in the mode of a shepherd–Yahweh’s contract herder. Although the imagery and idiom belong to the cautious traditions of Sinai theology, the psalm is unmistakably positive about David. It shows the sort of support of Davidic rule within Sinai theology that may have finally opened doors in Jerusalem to Micah’s message. Micah’s words may have found entrance into official temple circles by hanging on the coattails of the Asaphites’ work” (p. 127).