This would all be true if we were all genetically identical. However psychometrics has proven and now cognitive genomics is confirming that valuable mental characteristics have very large genetic components.
Intelligence is the capacity to achieve your goals. Intelligence is highly heritable. A goal of most people is to become wealthy. So people who acquire wealth tend to be much more intelligent than average, as wealth is graded on a curve. Thus though there is regression to the mean, their children will be more intelligent than average, and so worth more as employees and more likely to succeed even if they were put up for adoption.
This has unfortunate class implications, but putting cotten in our ears is not going to help. We must separate the normative from the descriptive. This is horrible and unfair. But natural selection is heartless algorithm literally running on death and suffering. We should not expect it to distribute capacities in a manner that is aligned with the prescriptions of our flimsy ideologies.
Wealth distribution would not fix this.
But let us seize the high-IQ alleles and distribute them to the proletariat!
Such thoughts are verboten now, even as our tools for such interventions get ever sharper and assortative mating magnifies these differences to a point where it is getting difficult to ignore.