Humans are our only model of the type of intelligence we are trying to develop, any other target would be a fantasy with no control to measure against.
Humans are extremely general. Every single type of thing we want an AGI to do is a type of things that a human is good at doing, and none of those humans were designed specifically to do that thing. It is difficult for humans to move from specialization to specialization, but we do learn them with only the structure to "learn, generally" being our scaffolding.
What I mean by this is that we do want AGI to be general in the way a human is. We just want it to be more scalable. It's capacity for learning does not need to be limited by material issues (i.e. physical brain matter constraints), time, or time scale.
So where a human might take 16 years to learn how to perform surgery well, and then need another 12 years to switch to electrical engineering, an AGI should be able to do it the same way, but with the timescale only limited by the amount of hardware we can throw at it.
If it has to be structured from the ground up for each task, it is not a general intelligence, it's not even comparable to humans, let alone scalable beyond us.