The grammatical shape of iḍāfah may remain unchanged while its rhetorical purpose varies. Good analysis separates identification by syntax from the intended contextual effect.
PurposeHow the relation is usedIllustration
BrevityCompact identification through a known relationshipصَاحِبُ الدَّارِ
HonoringDrawing on a respected associationعَبْدُ الْخَلِيفَةِ
DisparagementSelecting a relation for a belittling effectوَلَدُ الْحَجَّامِ
All the illustrations express a relation. What changes is the impression the speaker intends the hearer to form. Annexation can therefore be a means of rhetorical selection as well as definiteness.