The objection is that a singular noun conveys unity, whereas exhaustive inclusion involves multiplicity. The commentary's response does not assert unity and plurality of precisely the same feature. Singular describes the form or individual mode of predication; comprehensive meaning distributes the claim to each relevant member.
In “Every student can succeed,” “student” can remain conceptually singular while the quantifier ranges over the class. Singular representation and total extension belong to different levels of analysis.
This answer does not prove that every singular noun is universal. It establishes only that singular morphology is not, by itself, a logical obstacle to exhaustive application when the context supports it.