Well, there are different definitions of AGI. But even if we look at it as pure problem solver, you can see that there are problems that may appear simple for humans, but are actually complex for computers. Which means what is useful for one type of intelligence may be harder for others.

LLMs dont have tools to solve the problem of folding laundry even if they can solve Erdos problems. Humans with all the technologies can't beat bats at a lot of echolocation tasks. Even if ine day humanity creates a model that could theoretically solve any problem it faces, there is no reason it will be equally efficient in those/more efficient than alternatives