You would, but the movement is about both cleans and presses, unlike cleaning into squats which is about squats. See what I'm saying? In cleans and presses, a you clean the bar everytime you press the bar. You only clean the bar once to do squats, so its almost non-essential.
Also there's the weight disparity. I can squat a whole lot more than I can clean, but I can clean the relatively same amount that I can overhead press. So the two movements work well together in a mid to high rep volume workout plan.