That is the problem: the S-PN construction doesn't convey the sense that you contend for.Nonsense. both are S-PN constructions. The language is the same --
Ὁ θρόνος σου ὁ Θεὸς and κύριος στερέωμά μου
To say "Thy throne is God" equates the throne of the king with God, and is literally blasphemous, because the meaning then becomes not "Thy throne is of God" but "Thy throne is (as if) God".
Here the sense becomes "the King's throne is a rival to God's throne." Whatever figurative sense might be imputed is heavily overshaddowed by the far more obvious literal blasphemous meaning.
Whereas "God is my rock" is plainly figurative speech, as the sense cannot be that God is a rock in the possession of the speaker.