Classical writers speak of this as well, things like how inordinate and undisciplined appetites (not just for food, mind you; sex, too, and undue acquisitiveness of all sorts, for instance) darken the mind. What is inordinate and undisciplined is not proportioned or directed by reason. So, such character traits are rooted in fidelity to reason which means that not only do they avoid the aforementioned darkening of the mind by moderation of appetite, but the very character strength of being able to do so enables rational existence in other things.
Innate intelligence doesn't secure discipline. Indeed, it gives the person a bigger footgun and allows for more elaborate rationalizations of vice.
Regardless of what underlying trait it's actually measuring, the habituation factory is a big component of its supposed bias - that is, has your background taught you the kind of problem-solving habits that will help you to post the best possible score?
This question was asked and answered many decades ago in sociology. Researchers moved onto more interesting topics and fields. IQ tests measure g factor (https://en.wikipedia.org/wiki/G_factor_(psychometrics)).
> "It is a variable that summarizes positive correlations among different cognitive tasks, reflecting the assertion that an individual's performance on one type of cognitive task tends to be comparable to that person's performance on other kinds of cognitive tasks."
In other words people who are good at these tests are also good at real world tasks. Meaning IQ measures much more than one's ability to pass an IQ test. There are of course many examples of poorly structured IQ tests (including people re-taking the same IQ test and doing better at it the second time around). However a well-structured IQ test presenting novel questions (absent popular culture references and trivia) provides a very good approximation of the g factor in almost all cases. This means high IQ is highly correlated with things like income, unemployment, crime, homelessness, addiction, divorce, and many other objectively measurable life outcomes.
There is room for a philosophical debate about what g factor is, but it is beyond contest at this stage that g factor is real, and IQ almost always does a very good job of measuring it.
Sure: there's a battery of general cognitive tests, and if you smush data sets together a dominant factor will emerge. And?
Perhaps suggestive, but far from conclusive (I know you know this too). To me, it is suggestive that there is likely some other factor that may explain the relationship better, but then again, I am wrong more often than right, so what do I know? ;)
For example, compare that to growing wealth inequality, and I wouldn't be surprised if that is a potential factor. Less income = less access to care, less access to healthier food options, perhaps less time to for self-care, etc., and if wealth/career potential is gatekept by academic achievement, economic utility, or intelligence, then I can see the two, intelligence and BMI, being correlated, but not directly causal. Though, no study would give people large sums of money to improve their lives, so I doubt we will know for certain.