The “kings of the earth” who rebel against Yahweh are mentioned at the beginning of the Psalms, and Yahweh’s response is to install His own king on Zion (Psalm 2:2, 6). Then Yahweh’s king drops out of the picture for awhile. Yahweh is identified as King (Psalm 5:2; 10:16) but the Davidic king does not.
When the king reappears in Psalm 18:50, he’s in trouble, surrounded by enemies, and has to be rescued by Yahweh. Psalms 20-21 speak of the king and the Lord’s faithfulness in saving him. But then the Lord abandon him (Psalm 22), and the king disappears again for a time.
The long and short of it is that in the Psalms the Davidic king appears in the Psalter as a suffering king. Suffering is what Yahweh’s king does.