So your argument is:
Premise 1: Intelligent people are more likely to get high-paid jobs.
Premise 2: Intelligence is partially due to genetics.
Conclusion: People in high-paid jobs will have children who are, on average, more intelligent than those of people in low-paid jobs.
In addition you say: “most people in well-paid jobs would be considered middle-class.”
Thus you conclude that middle class children will be more intelligent than working class children, on average. Indeed, I believe you earlier said the conclusion was “unavoidable”.
It is certainly avoidable.
Consider 2 populations A and B, who do not interbreed if at all. They have the same level of inherited intelligence.
Suppose that those getting high paid jobs are drawn almost exclusively from group B. Group A is, for various reasons other than innate intelligence, nobbled when it comes to competing effectively for those high paid jobs.
However, all those in Group B can compete more or less fairly for those jobs. If premise 1 is true, those in group B who are more intelligent will more likely end up in the high pad jobs.
Given premise 2 we can conclude that the children of those in high paid jobs will be more intelligent, on average. In fact they will be more intelligent on average than those in either group A or B. (this is the bit anon is correct about)
Yet group A is not genetically less intelligent than group B. From the conclusion that the children of those in the higher paid jobs are more intelligent on average, plus the fact that those in group A fail to show up much in those jobs, it does not follow that the children of group A are genetically less intelligent on average.
So now we can see why the fact that e.g. black people fail to show up in high aid jobs does not entail their kids will be genetically less intelligent.
Other factors may be preventing black people from competing effectively for the high paid jobs. And in fact it’s pretty obvious what those factors are: cultural baggage, discrimination on basis of culture and skin colour, other factors determining intelligence affecting their final IQ, etc.
Anyone knowing this stuff would be bigoted or foolish to conclude that, given they fail to show up much in the high paid jobs, black people are innately less intelligent, (this would be true even if they have no other data about intelligence and race that led them to think black people are of equal innate intelligence).
But of course exactly the same kind of factors affect class too. There are many obvious reasons why working class kids with high innate intelligence will only rarely show up in the high paid jobs. My contention is anyone knowing that would similarly be bigoted or foolish to conclude that working class kids are innately less intelligent ob average, given their parents fail to show up much in the high paid jobs (even if they have no other data about intelligence and class).
However, this is where you, anon, pull, a fast one, saying, in effect: “Aha! but race is not defined by reference to holding high paid jobs, whereas class partly is. So that’s why it is reasonable for me to conclude – indeed the conclusion is unavoidable – that working class kids are less intelligent on average.”
So suppose we introduce a new category: black people not holding a high paid job. Call this group BPNHPJs. Note that BPNHPJs are actually defined in part in terms of their not holding high paid jobs (just like working class people). Can we now reasonably conclude that BPNHPJs are genetically less intelligent on average? Is the conclusion is "unavoidable"?
Clearly not. For if black people fail to make into high paid jobs for these other reasons, the two groups (i) BPNHPJs and (ii) black people will have the exact same membership.
And anon has already claimed that black people are not genetically less intelligent.
Clearly, given our knowledge of other factors playing a role in explaining why black people don’t end up much in high paid jobs, we cannot reasonably draw the conclusion that either black people or BPNHPJs are innately less intelligent.
But then the same must be true of the working classes too. We cannot reasonably conclude their kids are innately less intelligent. Not even if we actually partly define “working” class in terms of not holding a high paying job. That's just a bit of semantic sleight of hand from anon.
(PS I am away for a few days so maybe delay before I comment again...)