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You're first and last point are strongly related. Back when we were introduced into chess as kids, I was exceptional at it compared to most of the others, because I could use raw logic better than them. But once some started to train and I didn't, I predictably slipped behind. Based on my skill with other games and the fact that I started from a higher floor, I could probably keep being better than them, I just didn't focus on it. I liked other games more. If you investigated skill in different board games that all need broadly similar traits and talents, I'm pretty sure you'd find results akin to our IQ results: There is quite a strong correlation between them, and especially on the >1SD and >2SD level you find a lot of people who are just generally good at everything with mild specialisation. But to reach the >3+ SD and more, you need some serious over-focusing and specialisation to the exclusion of other things in addition to the naturally high general talent. Mind you, you somewhat misrepresent the state of the research AFAIK; Even the people at the top end for one category still tend to be significantly above average in other fields, they just aren't at the top end of everything simultaneously.
That's not to say that there aren't other skills critical for only one subfield, or even other relevant general skills. EQ, for example, really needs good face reading to work. Meaning if you have some degree of prosopagnosia, it will be much harder for you, even if you try to focus your intelligence on it. Likewise, if you think about problems in physical space, then a talent for innate 3d visualisation is extremely useful (something I relied on a lot when studying math; I always prefer to move everything towards geometry, which some other students didn't understand, while others also found it intuitively helpful).
Nevertheless, once I account for these other skills, I still use my general reasoning in everything. I use it to mentally move and manipulate shapes, I use it to understand people, I use it to time-plan.
For another example, memory is also a fairly general skill, though not equally so for everything, and I have always really noticed the impact of focus there. Back when I played Battlefield Bad Company 2, I memorized every single weapons traits: Damage, mag size, recoil, delay between bullets, reloading time, even the exact shape of the damage-distance curve ... Same goes for other games. Meanwhile my social memory used to be awful, to the degree that I once forgot my own name when introducing myself (awkward!). I used to tell myself that these are just totally separate things and that it's not my fault, but now that I'm a dad and office worker, I find myself having much less trouble remembering social details about various people, as long as I think they matter. In the same vein I have less patience to remember all the detailed mechanics of arcane games. It's increasingly clear to me that I'm merely re-directing a general skill towards the things I care about, as opposed to there being different skills.
I like your examples of face-reading and 3D visualization. Doesn’t it sound a lot like these are distinct mental capabilities that certain people have distinct from their other capacities? And the idea of using your visualization skills to understand other mathematical realms suggests that your “general” intelligence in this case is informed by your ability to generally apply a more specific talent - and this works for students in proportion to their capacity with that specific talent. Presumably the students who don’t get it but who are still good at the subject are channeling a different underlying ability.
Flipping it around heavily, the memory example is also great. I’ve seen this as well: pretty much everyone I’ve met who was not heavily brain damaged has had some category of thing which they remember quite a lot about, corresponding tightly to their areas of interest. Presuming that “my results on a test” can be an area of interest, does that mean that the means of measuring abilities can identify divides in capacity when it’s really just a divide in focus?
My biggest sense for IQ and intelligence is that we just don’t really have a good idea of what’s going on. We’ve found certain capabilities which are confusingly harsh yes/no values, like the internal monologue and the ability to envision things, considering that there is no evidence that someone is one or the other without asking them: you would expect the difference to be night and day, like it is for children and adults! But we’ve also found certain capabilities that appear to be a single thing, like memory, but which express themselves in such radically different ways that you’d be forgiven for thinking they were entirely different capabilities, and which differences are immediately obvious upon meeting someone. That is, our intuition struggles to break intelligence down into real atoms, and naive external analysis carves at awkward joints.
To the extent I have a point, it’s that intelligence is way, way more complicated than the IQ test model makes it out to be, that we know effectively nothing about it, and that we should be really, incredibly humble about our proclamations about it. We’re all out here debating the four humors; that’s how bad it is. People back then would talk very confidently about the humors, and now they look ridiculous. They may have been smart, but the reality was that they were fools, and they could have been less foolish by being honest on what they didn’t know.
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