(I'm not an expert, and my opinion is formed from following that blog.)
In terms of your example, I'm not sure what "there is more genetic diversity among Africans" means. What is the measure of diversity here? Why would we necessarily expect that measure to mean "more races"?
(I didn't downvote you, by the way. Not sure why so many people on HN seem to enjoy downvoting any discussion on certain topic. :/.)
Thank you, I think I get it now that I've read through those.
I think that graphic illustrates what I'm saying fairly well. The non-African populations in the graphic are all grouped at the lower left corner. There are distinctions between them, but less than there are among the African groups.
The current (a key word, as which people go into what race has changed a lot in the recent past) social grouping of races would have us believe that the small purple group hanging off the end is one race, the pinkish group next to it is another race, the red group next to that is another one, the small green group next to those is maybe separate or maybe a subset of one of the others depending on who you ask, and then all the other groups are classified as "black." This pretty clearly makes no sense if you're trying to classify groups genetically. Why should that yellow group sticking way up from the rest in the top right corner be lumped in with so many other groups?
And getting back to your original point, some of the modern sense of race is pretty unsophisticated, like "people with dark skin". That encompasses many distinct populations.
But I think older racial thinking was actually more nuanced, and would consider many different attributes when categorizing "races", which maps pretty well to distinct populations, which maps pretty well to stuff like PCA.
E.g., I suspect the thinking that went into something like like this
The examples I gave should be sufficient to demonstrate that there are at least major discrepancies between the two.