It's because there aren't distinct populations like you perhaps imagine them being, it's more like a smeared colour pallet where one area might be a bit more red or a bit more blue but it's hard to say a specific area is pure blue. The distinct features or populations exist as statistical probabilities based on likely ancestry for a given area. Any given individual in a population probably doesn't express all the "unique" features, but over the total population those features are most prevalent.
Regarding Neanderthals and denisovian populations, they were probably more like what we'd call subspecies in other animals than truly distinct species from modern humans, isolated long enough to build up some unique genetic markers but not quite long enough to be fully separate.
Not really, because it doesn't guarantee any specific individual in that population has any of the populations likely traits, it's only useful in aggregate for things like prioritising screening for certain genetic conditions for people of particular back ground. It's useless to determine if someone will be an excellent sprinter or a fighter pilot because ultimately you still have to test every individual anyhow and it doesn't really tell you anything about the "tree" of human evolution which is really a bunch of thick branches all tightly fused together into an indistinguishable single branch.