It makes sense if you believe in evolution. As a population diversifies and spreads out of its center of origin, the populations doing the moving are smaller than the parent group and so have a smaller genetic pool within which to work. The parent group retains the larger genetic pool and with it the greater diversity. As man was supposed to have originated in Africa, it makes sense that Africa would have the greatest genetic diversity and genetic testing would seem to indicate it.
There is a correlation with linguistic diversity. There are more language families in Africa than anywhere else.
Superficially to Europeans like us, it appears that Black Africans look more alike than we do, but that is probably a distortion created by our own perspective. We probably look more alike to them than they appear to resemble each other. But morphological differences or similarities do not have to reflect genetic realities.
A very good point. in addition to your point, we are all intensely tribal as it was very necessary for us to recognize people who are the same and people who are different. Before living in Southeast Asia, all east and Southeast Asians look pretty much the same to me. Now, with a high degree of accuracy, I can distinguish not only between Han Chinese and Thai (it is easy), I can tell a Maeo from an Akha or Karen. From facial distinctions, I can tell the region a person comes from and very clearly distinguish a Burmese from a Lao from a Khmer.
It is fascinating to me and I imagine people in America could, at one time at least, distinguish ethnic background just by look (Irish from Swede, from German) with equal precision.