when you get to the top of your knee lift, your weight with then come down. when the weight comes down, you must be in a position to catch all that force in the ball of the back (or post) leg foot. when this happens the knee is typically bend in an athletic position. the back foot must be absolutely stable and in a position to catch and manage this weight shift into the ball of the back foot. i think sandy koufax is right and positioning the ball of the back foot just in front of the front edge of the rubber is extremely stable and lines up the bones of the ankle and shin so you do not lose force in the bones of the ankle attempting to manage this weight shift while the back foot is flat in front of the rubber (especially if the mound is made of sand or loose dirt or has a massive hole in front of it). it is much better to pitch from the front edge of a stable rubber lining up the bones of the ankle than trying to stablize the back foot flat in front of the rubber using the side of your foot on loose dirt. koufax asks if you were moving a 100 lb rock with your foot, you would push with the ball of your foot at an angle, not the side of your foot pushing in a straight horizontal plane.
when the weight shifts to the ball of the back foot, the hips are moved as far forward toward the plate as possible. this is leading with the hips and creates a < in the back side of your body. this is an extremely powerful position if you are strong through the core of your body (shoulders, trunk, and hips). it is not uncommon for hard throwers to also counter-rotate at this time, and tilt the front shoulder up much higher than the rear (throwing) shoulder. i encourage this position especially in young pitchers (the koufax clip shows this as well as it can be done).
after the bracing against the rubber with the ball of the foot, getting the hips out and tilting/counter-rotating as far as possible while maintaining balance, you begin to move toward the plate. as you move toward the plate, i think there is an additional push, shove. brace - (whatever is politically correct) by extending the ankle as you move down the mound. i think it is the only way a pitcher can stride farther than his height. this is the equivalent of pushing a moving merry-go-round while standing beside it to make it go faster. if you time the push correctly, you can get the merry-go-round spinning very fast through a series of small pushes. if you time the contractions of your body correctly, you can do the same thing to throw a baseball.
the back knee does not extend, but i see the ankle extend as pitchers move toward the plate. i do not see a passive fall toward the plate. i see placing torque on the core through counter-rotation, tilt and releasing this torque and force in a progression from the ball of the back foot, to the front foot, then through the body and into the throwing arm/hand and ball.
when the front foot hits the ground, you move the shoulders in front of the hips, and rotate as late as possible to maximize momentum and/or force into the throwing arm and hand. the front leg firms up and can extend to a locked position just after release to maximize the force coming from the ground through the front foot as it braces up.
i think this is how you throw using momentum, leverage, and force generated through movement and coordination of the big muscles of the body.
many will disagree with this, but i go by what i see, and has worked for me teaching pitchers for over 10 years now, and intensive study of video of pitchers who threw hard for a long time.
may be wrong but it’s what i use. you’re welcome to it.