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.
I am taking a step back and questioning the necessity and reasonableness of giving such definition in the first place, not arguing against its possibility. Of course you can define it however you like, I just think it won't take you far for the reasons I have given.