It can only simulate the outcomes of intuition in its training set.
The likely uncloseable gap is that some intution is unspoken, literally felt by the brain's default mode network.
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.
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 intution 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.
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.