If you can find none, is it not the proof that our intelligence is general?
There's also problems of self reference. A Turing machine may be able to solve the halting problem for pushdown automata, but it can't solve the halting problem for Turing machines. Whether or not we're as capable as Turing machines, there's a halting problem for us and we can't solve it.
I'm restricted to mathy spaces here because how else would you construct a well defined question that you cannot answer? But I see no reason why there wouldn't be other perspectives that we're incapable of accessing, it's just that in these cases the ability to construct the question is just as out of reach as the ability to answer it.
You may have heard talk about known unknowns and unknown unknowns, but there are also known unknowables and unknown unknowables, and maybe even unknowable unknowables (I go into this in greater detail here: https://github.com/MatrixManAtYrService/Righting/blob/master...).
In any case, I don't think it's ever valid to take one's inability to find examples as proof of something unless you can also prove that the search was exhaustive.
Instead of AGI, we should call it AHI: artificial human intelligence, or SHI: super human intelligence. That would be much clearer and would sidestep the generality issue.
Also, no one person invented the calculator. The calculator is the culmination of hundreds or even thousands of years of invention. It’s not like the knowledge or creativity is in each of our brains and we could each build a calculator given the requisite materials. It took thousands of lifetimes of ingenuity. So there’s another answer to your question of things we aren’t efficient at solving: building a calculator.
If we had more intelligences around to compare with I think we'd find that some are "more intelligent" in that they have all of our capabilities, plus some. And that others are "less intelligent" in that we have all of the capabilities that they have, plus some. And then there would be the "differently intelligent" which have at least one capability that we don't and which lack at least one capability that we have.
Under this lens, I don't know if there's much utility in fine grained comparisons of intelligence re meters and millimeters. The space is discrete: subsets, not metrics.
I don't know if you could ever prove something like this (or maybe we just lack that capability). It seems more like an axiom-selecting notion than something to be argued. Anyhow, it's what my gut says.