According to dual processing model, intuition isn't some trick factory that magically produces instantaneous correct assessments from faulty data.
Intuition is part of brain's automated response to quickly evaluate some situation. It does so at the cost of accuracy, and it's superbly more prone to errors, bias, misunderstandings, misinterpretations, inaccuracies, overestimates etc. than what the same person can accomplish by really thinking about it.
Also, people don't usually distrust their automated responses unless specifically having learned to do so in a specific situation. Instead, anything that comes as an automatic response is more likely interpreted by the person as self-evident, correct and true.
So, here we have the explanation for N-users self-proclaimed supremacy. It's illusion, perpetuated by overreliance to system that is critiqueless to begin with. One simply doesn't introspect with system 1 - not at least objectively.
N users are doing just fine. So what's the whole picture?
In modern ages, industrial, information age etc our living environment has changed way faster than our pre-historic system 1 has adapted. We're really better off not trusting our system 1 for the most part - this is where education comes in. Endless memorization about the hazards our ancestors could never have imagined. High voltage? Bad home insurance plan? How to select your president?
Good news is that system 1 can be trained. It will still not do things when asked, but at least the automatic evaluations it give will be more specific, accurate, useful, relating more to the true circumstances of the situation, etc.
So, which comes first? Does one decide to train their brain to become N? Or.. are N just people who are a little bit more resistant to formal training and / or memorizing, and instead train their system 1 a bit more? I don't know.