I think there were probably thousands of varieties of hominid originally, for example varieties AA thru ZZ. If you look at the variety of living languages in the world today you will find the most primitive cultures consist of a few small villages of just a few hundred people, separated by dozens of kilometers. These small populations speak unique languages, and engage in tribal warfare with other villages just like the more primitive primates. There is little doubt why Darwin realized our origins. Indeed, the very terminology of language (living versus extinct) is strongly suggestive of evolutionary trends, ie. natural selection.

I think it's more likely that the particular variety of humans that were at first geographically isolated in Africa developed the ability to live in a variety of climates, and simply moved out of Africa. They then proceeded to wipe out all the other varieties of hominid that inhabited other regions of the world. So what we are left with is hominid species "P" out of what was originally a wide spectrum of traits. The only ones left are those that do not compete with us directly, variety AA (perhaps chimps, apes, etc), and variety ZZ (monkeys, lemurs).

In Darwinian evolution, the individuals that have the most offspring are most likely to be the only ones with descendents. Their descendents will populate the world, and all other lineages will be dead-ends. It is a long drawn-out process that takes thousands or millions of years. But eventually all the living members of a species can be traced back to a single individual in the ancient past. That's why, as you say, "We all came from Africa". In another 100,000 years I'd bet that will change to "We all came from China", or "We all came from India".