An exhaustive exception generally does not pronounce the overarching category. We reconstruct it to explain the semantics; this does not mean it is overt in the sentence.
مَا ضَرَبْتُ إِلَّا زَيْدًا
I struck no one except Zayd.
Supplying “anyone” conceptually is a way of revealing the excluded alternatives, not a claim that “anyone” is literally present in the utterance.
The implied class changes when illā is followed by a manner or time. A single reconstructed noun cannot be forced into every construction.