I understand what you are saying and sort of agree the premise but to be pedantic, I don't think any robot can clean a kitchen without doing math :)

Intelligence doesn't have to be embodied.

For it to be AGI, it needs to be able to manipulate the physical world from it's own goals, not just produce text when prompted. LLMs are just tools to augment human intelligence. AGI is what you see in science fiction.

It also has to be able to come and argue in the comments.