The argument works just as well

I feel like the argument is slicing the problem up and presenting just the worst bits, when we need to consider the net effect on everything. This reminds me of a bioethics debate about testing error and base rate of rare lethal diseases: if five times as many people have disease A than disease B, but they look similar and the tests only offer 80% accuracy,* what should we do if the treatment for A cures those with A but kills those with B, and vice versa?

The 'shut up and multiply' answer is "don't give the tests, just treat everyone for A," as that spares the cost of the tests and 5/6ths of the population lives. But this is inequitable, since everyone with disease B dies. Another approach is to treat everyone for the disease that they test positive for- but now only 4/5ths of the population lives, and we had to pay for the tests! Is it really worth committing 3% of the population to the graveyard to be more equitable? If one focuses on the poor neglected patients with B, then perhaps, but if one considers patients without regard to group membership, definitely not.

*Obviously, the tests need to be dependent for 80% to be the maximal possible accuracy.

And people didn't notice the good blacks should be in the office and promote them at a higher rate to make up for it, either.

I don't know if it's possible to test this, and specifically it's not obvious to me that we need racial bias to explain this effect. That is, widespread cognitive stratification in the economic sphere is relatively new (it started taking off in a big way only around ~1950 in the US), and if promotions were generally inefficient, it's hard to determine how much additional inefficiency race caused.

These comparisons become even harder when there are actually underlying differences in distributions. For example, the difference in mean male and female mathematical ability isn't very large, but the overwhelming majority of Harvard math professors are male. One might make the case that this is sexism at work, but for people with extreme math talent, what matters much more than the difference in mean is the difference in standard deviation, which is significantly higher for men. If you take math test scores from high schoolers and use them as a measure of the population's underlying mathematical ability distribution and run the numbers, you predict basically the male-female split that Harvard has, which leaves nothing left for sexism to explain.