The post-exception element

Restriction by Fronting and the Rhetorical Contrast of Qasr Methods

مَا زَيْدٌ إِلَّا شَاعِرٌ
Zayd is only a poet (within the relevant contrast).

Here the element following illā is a description. In “None is in the house except Zayd,” it identifies a person instead. The contrast under consideration is different.

ExpressionContrast domainExclusive counterpart
mā Zayd illā shāʿirZayd's descriptionsPoet
mā fī l-dār illā ZaydOccupants of the houseZayd

Grammar is important, but the semantic relation must first be identified.