Ok, so I recently learned about the hierarchical model of intelligence, which to explain it means that intelligence is best conceptualized as a hierarchy and can be envisioned as a pyramid in which there are some 70 narrow abilities at the base, 8-10 second order factors at the next level(reasoning, verbal comprehension, numerical ability, spatial ability, word fluency etc) and a single general factor or g at the top.

So my question is that if g supposedly underlies all these second order and lower order factors, then why isn't mastery in one factor intercorrelated (most of the time) with another factor? Take word fluency and verbal intelligence as an example: there are people, who are very proficient in writing,debating and articulating their thoughts in a very good manner, but absolutely suck in things like math or physics or vice versa. I think we've all met people like these and these people make up a large majority of the population. So essentially they're very good in one field that g supposedly underlies, but at the same time suck at another thing that g underlies.

I'm having a hard time wrapping my head around this inconsistency, since there's no doubt that verbal intelligence is pretty g-loaded, so you would expect people who are good at these things that are highly g-loaded be equally good in other g-loaded factors such as problem solving, reasoning (math by proxy), but this isn't the case. It seems that in spite of a few polymaths most intelligent people are only proficient in one area and