Yes they do but wouldnt they prefer a weak one? If there was a three legged sick doe and a 250 peak health buck standing in a field which one will the coyote go for? Here's a good source of information.
Predator Prey relationship All I'm saying is that natural predation does a good job of selecting the weak and therefore making the prey stronger better evolved.
Your making your self god when you say that you know better which animals should die than a coyote