Sure they do? When people do a standing jump, they first crouch lower to the ground. An arrow is pulled back on the bow before fired. A ball pushed uphill will roll uphill before stopping and rolling downhill.
"Anticipation" in character animations is a source of persistent friction between game programmers and animators because if incorporated as part of user/player action it simply kills responsiveness. OTOH being able to see NPCs prepare to do something (like pulling the bow) is incredibly useful.
Most living beings aren't trying maximize performance, they're trying to maximize survival. That crouch gives away that you're about to jump, and it allows prey to avoid you more easily or predators to adjust their attack to counter for it. A rabbit trying to get away from a predator simply bounds away in its given direction without giving away what its doing.
Even the human jumping example again... Suggesting people only bend their knees for performance would mean the "normal" way of jumping involves keeping your legs straight at all times and using your ankles/toes for all your thrust?