It can only simulate the written outcomes of intuition in its training set.
For sure, some of those written outcomes are a good guide to reaching the outcomes of intuition.
But the likely uncloseable gap is that some intution is unspoken, literally felt by the brain's default mode network and by parts of the prefrontal cortex.
LLMs basically never shower, do the washing up, kick their foot in the dirt while sitting on a park bench with a coffee: the domain of the default mode network. And they never sit frustrated looking at things, guided by their long experience, with the itchy brain feeling that there is a solution before they can even say the words.
A lot of this stuff happens to us deep down, way outside of the reach of words. And as a result, some aspects of intuitions are just never described in words.
I'm sure the training data of LLMs contains a lot of those things, though.
But they are not the things themselves — they are incomplete representations; just words that approximately describe the application of that intuition to the problem at hand.
Think about how you visualise complex code projects in your mind — how it's not quite diagrams or buildings or words but multiple things in a sort of multi-dimensional, itchy space that is satisfied when a really good implementation appears. Think about how often the code you have built retains that wordless shape long after you wrote it down. Think about how impossible it is to adequately describe it.
The downside: the model doesn't always have words to describe what it's feeling.
Those outcomes are more easily averaged and we are after all talking about artificial intelligence. And for a coding agent… perhaps this is the right tradeoff.
I just think it's important to note, every now and then, that words aren't feelings or thoughts, and that an author's next book cannot be calculated from only the words of their previous books, etc. Basically we should understand that the reasons why we can't generalise from "it can design processors, write code and solve maths" to "so human-expert-quality writing and web design should be easy enough" are probably rooted in differences like these.
(as it would apply to a human software engineer also)