Here's a video of Boston Dynamics' "Cheetah", a running four-footed robot.
Note how the feet touch the ground. Without a wrist, the straight leg nearly has to drag the ground when it is pushing off. Further, as the angle steepens between the leg and the ground there's 1) more opportunity to slip and 2) reduced ability to push off.
Here's a real cheetah. Here's a picture of cheetah anatomy. Note how the forelegs are kept straight and the paw is kept bent. Cheetah's run on their fingers (paw) bending at the metacarpals. A human hand is organized differently. Hold out your hand. The fingers are the carpals. The bones of the back of the hand are the metacarpals. The metacarpals join back to the wrist. The foot organization is similar.
Now, look at the anatomy image of the cheetah. It's "fingers" splay out in front if it. The metacarpals bend upwards and are supporting weight directly into the wrist. When the cheetah moves, the "finger" stretch out flat-- the paw-- the metacarpals stiffen and the fingers act to grab the ground. The wrist stiffen as well and the whole arm moves back. Then, when the paw comes back up the wrist and metacarpals unlock and the whole assembly swings up and out of the way so that it can be brought forward.
The same motion in the back.
Here's Boston Dynamics"Big Dog." It has a wrist but instead of metacarpals it has a pole and no paws (no fingers.) Better than the BD cheetah but still a long way to go.