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I don't know too much about HBD, but I would guess that the most important trait for them is intelligence. And maybe aggressivity, impulse control, ability to cooperate with non-relatives, and this kind of necessary-for-civilization things. (You can ignore other traits, such as eye color or lactose tolerance, they don't make a big difference in modern society. So you'll buy a different box of milk, big deal.)
Mathematically speaking, if you could measure something to million decimal places, it is very unlikely that the averages for different populations would be exactly the same. But in real life, a difference of 1 IQ point does not make a huge difference. So the question is whether the differences are large enough to matter in real life.
Humanity split from our common origin about 10000 years ago. It seems like enough time to make significant changes; for example, mere 1 IQ point per century could accumulate to a difference of dozens of IQ points below distant populations. On the other hand, humans were already shaped by evolution millenia before they split, so maybe most possibilities of cheaply gaining yet another IQ point were already exhausted before we split. I don't feel certain enough to make a hypothesis either way.
So we should solve this question empirically, and then we get into problems -- the old research was unreliable, and the new one is not done for political reasons. So I still feel like the answer could go either way.
This question is solved empirically. If you look at the data it's really obvious. There is NO serious research which claims that all populations have essentially the same IQ.
You're off by an order of magnitude or so.