I am trying to use an outside view here, because I find the inside view too limiting. The best I can do is to construct a tower of comparisons between species vastly different in intelligence and conjecture that this tower does not end with humans on top, a Copernican principle, if you like. To use some drastically different pairing, if you agree that an amoeba can never comprehend fish, that fish can never comprehend chimps, that chimps can never understand humans, then there is no reason to stop there and proclaim that humans would understand whatever intelligence comes next.

Certainly language is important, and human language is much more evolved than that of other animals. There are parts of human language, like writing, which are probably inaccessible to chimps, no matter how much effort we put into teaching them and how patient we are. I can easily imagine that AGI would use some kind of "meta-language", because human language would simply be inadequate for expressing its goals, like the chimp language is inadequate for expressing human metaethics.

I do not know what this next step would be, no more than an intelligent chimp being able to predict that humans would invent writing. My mind as-is is too limited and I understand as much. An AGI would have to make me smarter first, before being able to explain what it means to me. Call it "human uplifting".

Do we have some reason to expect its goals to be more complex than ours?

Yes, if you look through the tower of goals, more intelligent species have more complex goals.

It's been my experience that the more sophisticated and intelligent someone is, the more intelligible their behavior tends to be.

It has not been mine. When someone smarter than I am behaves a certain way, they have to patiently explain to me why they do what they do. And I still only see the path they have taken, not the million paths they briefly considered and rejected along the way.

My prejudice therefore says that the goals of an AGI would be much easier to understand than, say, my own.

My prejudice tells me that when someone a few levels above mine tries to explain their goals and motivations to me in English, I may understand each word, but not the complete sentences. If you cannot relate to this experience, go to a professional talk on a subject you know nothing about. For example, a musician friend of mine who attended my PhD defense commented on what she said was a surreal experience: I was talking in English, and most of the words she knew, but most of what I said was meaningless to her. Certainly some of this gap can be patched to a degree, and after a decade or so of dedicated work by both sides, wrought with frustration and doubt, but I don't think if the gap is wide enough it can be bridged completely.

I find the line of thinking "we are humans, we are smart, we can understand the goals of even an incredibly smart AGI" to be naive, unimaginative and closed-minded, given that our experience is rife with counterexamples.