Women, in general, prefer tall men. This is an example of “sexual selection” which is also part of “natural selection”. The fact that it is female humans doing the selecting and not female peacocks doesn't make it any less “natural”.
Evolutionary Biologists have long recognized the role of violence in human evolution. There is no doubt that among all the apes, we are the most carnivorous, the most violent, and the most murderous. Those changes are understood by Evolutionary Biologists to have come about via evolution through natural selection of genetic variation. And yes, natural selection includes war.
The theory as “popularly described”, as understood by you ( or MIS-understood by you); may well not “add up”. But that is a lack of your understanding, not a lack on the part of the theory.
By your definition, what isn't natural? What's the point of even having the word natural if it includes human activity?
Tallness is a marker for above average ability to provide. Tall people are not just taller, but in general are wider and deeper, and so are their brains. Tall people tend to make more money, not because they are taller, but because they are smarter.
Many cosmetic traits in humans were cultivated by mothers favoring them in their children, not from mate selection. White skin, blond hair, and blue eyes are examples. It's hard to imagine in modern times but for most of our past mothers had to choose which child survived because food was not reliable. If a mother had 6 kids, one with golden blond hair, the rest with brown, the blond was favored and had a better chance of survival. Many white children are born initially with blond hair and blue eyes, but these traits are free to completely change once the child has successfully bonded to the mother. While men also like blond hair and blue eyes surviving into adulthood, they'll pretty much mate with anything and they were not the primary driver of these cosmetic traits.