Well imho, it's a bit of a fundamental problem for a certain aspect of the meaning of "to intuit".
Since we're quoting Douglas Adams in this thread, I'll mention something I posted a while back, with his writings as example. After Douglas Adams passed away, somebody was tasked to "finish" The Hitchhiker's Guide to the Galaxy :
> And Another Thing... is the sixth and final novel in The Hitchhiker's Guide to the Galaxy series. Written by Eoin Colfer with the blessing of Douglas Adams' widow Jane Belson
Being a rather big fan, I immediately bought and read this novel and I have to say that Eoin Colfer did a really really great job, nailing the tone, humour and writing style of Douglas Adams.
IMVHO, he did about as good as anyone could reasonably expect someone to do, when given this task. It was big shoes to fill, and I was impressed.
But it just also wasn't good enough, in a weird way that I found hard to put my finger on at first.
The thing is that Colfer was doing the tone of voice, even came up with somewhat new jokes perfectly in the style of, etc etc. And for the sake of argument let's say he was able to get "arbitrarily close".
But there was always one thing he couldn't do: Actually make something new happen, make a new kind of joke, do a real plot twist, a big reveal, stuff like that. Because then it would deviate from Douglas Adams' work too much.
However, if Douglas Adams was still alive, this limitation would not apply to him: he could make a new kind of joke, do a plot twist, big reveal, and it would become canon.
This the best "good faith" argument I can present for how LLMs lack "intuition", in some sense. Now "intuition" is not a very exactly defined term, but I'm arguing that the thing I'm describing here, is at least a part of intuition, that an LLM fundamentally can't reach (until they start getting their own volition, which I would prefer they didn't).
To address your question:
> Surely the AI can complete the prompt “Generate new research questions based on these observations”?
Yes I imagine it could do that very well. But it would still need a human to decide if the research questions are "relevant" or "within scope" of what the human wants (a.k.a. their volition). Without that filter, the research would just bloom out exponentially, with more and more questions nobody was asking.
And yes, up to some point that "blooming" behaviour is a useful aspect of research, the exploratory aspect/phase, but at some point you need to get back to the "synthesis" aspect/phase, to distill all the explorations back to "stuff that matters". And just like Douglas Adams vs Eoin Colfer, only the human who wants to know something, can decide to widen or change the domain of that synthesis, but if the LLM were to decide this (outside of exploratory phase), it would actually be considered the wrong answer.
And this is not at all to say you can't do research with LLMs, obviously you can. But this is just a thing they can't do, on a real philosophical level. I'm also not saying you can't work around this limitation, you probably can, I'm just saying it exists.