Studies show that there is a lot of overlap in technical fields.

You have a lot of things to explain, then! Like the fact that some people are able to memorize entire deck of cards, but have a poor memory in real life (can't forget where they put their keys!). People learn by chunks in their fields, but most of the time, once they encounter a scenario that's too unfamiliar they are completely lost. I mean It's obvious and It's normal (eg: memorizing random letters vs memorizing complete sentences).

Another thing you seem to forget is that the brain is a lot less powerful to solve and remember boring things. If the IQ test is boring (it will probably be), I'd probably struggle a lot more, than saying studying/solving something interesting.

They show that on average if you are good at math then you are good at science.

Heh, then a lot of people I know are the exception too. Good to know. But again, you're excluding the fact you'll perform worse at things that don't interest you. I'm really curious by what you mean by "on average"...

Obviously there is some variability, but when you measure groups of people it is the most accurate measure of test scores of anything ever tested including wealth, parental education

Then IQ is really inaccurate or everyone must score terribly in this aspect. Seeing how parental education is in a terrible state right now, every parent forcing their kids to go to school and don't hesitate to become the number 1 enemy of their own child... If the only people scoring high aren't unschoolers, I consider your metric VERY inaccurate for this aspect.