AGI is the persistence of a technoscientific myth of contact with the superhuman at the heart of a secular enterprise; an allegory of faith in a disenchanted universe.
I don't think such an arbitrary definition is useful since it would lack specificity and reduce phenotypic plasticity to a set of supposedly human-exclusive measurable objectives. The boundaries of human beings are blurry. If you want to study a brittle abstraction go on with GI.
So your argument is that there's no GI because GI can't be defined? Hence your statement 'there's no GI' has no truth value. You don't know if it halts.
No need to go that far into the misadventures of the first taxonomists (species, a core concept of biology is not free of problems), since there are good modern arguments on the problems of categorical definitions of cognition.