This doesn't really answer the question -- how come there are usually only a few clearly defined species that descended from this common ancestor? Why isn't there a spectrum?
I don't know anything about the phylogenetic tree of humans and our cousins, but I assume that at some point there was a spectrum (e.g., Neanderthals), but at some point the others got wiped out, without humans splitting any further. Perhaps this is due to the global mobility of humans? What do biologists think?
The most intense form of competition is that from your own species, nothing else requires exactly the same conditions/ecological niches/resources. The less fit individuals are out competed (dont breed, or die), and the species as a whole is "pulled" in a certain fitness direction that is more optimal.
The reason speciation arises is complex, but its often due to different subgroups of a species exploiting different niches, and thus experiencing differing fitness pulls that eventually give rise to new species.
There are no "intermediate" species because they fit more poorly into either niche occupied by the two other species, and thus are out competed or dont arise in the first place.
I don't know anything about the phylogenetic tree of humans and our cousins, but I assume that at some point there was a spectrum (e.g., Neanderthals), but at some point the others got wiped out, without humans splitting any further. Perhaps this is due to the global mobility of humans? What do biologists think?