The problem is that "death of the weakest" is a much better way of describing it - although possibly not so PC to teach in the classroom. The reason why people think Cheetahs evolved to be fast is because they equate it with the ethic of hard work, rather than the real reason - slow cheetahs don't eat and therefore die before breeding, fast cheetahs eat and get to breed.
Without meaning to start yet another internet debate/flamewar about evolution, I often wonder whether the strong protestant work ethic in the US is also the reason why evolution is so poorly understood there. Because "death to the weakest" involves no agency, no self-improvement or hard work.
EDIT: Just to avoid to confusion (as there seems to be some!), I'm not talking about the mechanism of evolution, purely the actual phrase "survival" and what it means to people when it's mentioned, the implication of agency that goes along with the word.