Immunological phenotypes of the paleo-asian indigenous population was inferior to that of Eurasians due to both the PA originating from fewer ancestors (=less diversity) and not being continually evolved by being exposed to diseases. Hence, they died as flies while Europeans only got some weird veneral diseases in the "exchange".
Africans, however are a completely different story. There is a reason african slaves were brough in to replace the dying indians in the carribean and elsewhere. Genetically diverse as no others on the planet, and evolving in a nasty tropical stew of disease does that.
This, the nasty climate* and the tropical diseases were reasons enough to keep Europeans out of Africa, except the very sparsely populateds south African region, which also has a much better climate and much less tropical diseases.
* Where do you find significant populations of white people today that you wouldn't yesterday?
Southern south America, northern north America, Australia, far-eastern Asia and and to a lesser degree southern Africa. All these have few or no tropical diseases as well as a climate that would not be completely out of place in Europe.
To put it simply, we are not built for the tropics. Africans are, with the bantu-populations present in south Africa arriving only 50-100 years earlier than Europeans, depending on source and not "developed" to that environment since the original inhabitants were the physically much different Khoisan-peoples.
In theory, most of the south-African dry climate zone could've been colonized by whites, but incursions into the tropics requires modern medicine... And killing of the native would require un-modern ideology/culture.
The boers were too few to establish a powerful enough state to do something even remotely along the line of the American independence, thus they came under the rule of an European power. Had they been more from the beginning things might've been different though I havent seen any even remotely realistic scenario based on this pretext. Would be interesting though to see the Brits get routed and Rhodes getting what he deserved...!