Since LLMs aren't designed for this there's a whole post process to try to make them amenable to this use case, but it will never plug that gap
They don't have to be perfect, they just have to be better than humans. And that seems very likely to be achievable eventually.
[1] LLMs are already better than humans in terms of breadth, and sometimes depth, of knowledge. So it's not a problem of the AI knowing more facts.
We're desperate to keep seeing ourselves as unique with key distinguishing features that are unreproducible in silicon, but from my long experience with computer chess, every step along the way, people were explaining patiently how computers could never reproduce the next quality that set humans apart. And it was always just wishful thinking, because computers eventually stopped looking silly, stopped looking like they were playing by rote, and started to produce "beautiful" chess games.
And it will happen again, after the next leap in AI, people will again latch on to whatever it is that AI systems still lack, and use it to explain how they'll "always" be lacking... only to eventually be disappointed again that silicon can in fact reach that height too.
Humans aren't magic. Whatever we can do, silicon can do too. It's just a matter of time.