the left hook is a combination of things, to pivot or not to piviot is up to the situation. you should allways piviot with your left foot. though whether or not your piviot your body is a diffrent situation as you have to wind your body into the piviot by throwing a right straight, a right hook, or slipping to your left. if you just wind up your left for no reason your opponet knows something is coming from your left unless your fainting. so theres situations where you might not want to piviot your body like say after a jab or after you just threw a left hook. for these situations i reccomend just dropping back your right shoulder whirling your left shoulder pivioting your left foot and throwing a tight left hook with the palm facing down. this kind of hook needs to be tight for any power and since its tight the palm needs to face down. then theres the falling left hook where you take a step to your right with your right foot as you throw the hook then immediatly return your right foot back to stance as well you can either piviot your left foot with it or just push off with your left foot. the step squares out your body so you can piviot into the left hook with out winding it up and since its a falling step its got your entire body weight behind it. (fulmer vs robinson ko if you want to see this one in action)
Berserker: I also can pivot my hip just fine without pivoting the foot. When i go from a left cross to a right hook (im a southpaw) my hips can move almost 90 degrees without pivoting the foot, and they return nautarlly and very quickly after the punch to a nuetral position. What you will find though, at least with me, is that your knees are pivoting, or moving to a different angle. This allows the hip movement. I guarentee that every pro that says to pivot will have footage of him throwing that hook without pivoting. I agree with a very early post from RDJ, it depends on what you want to acheive with the hook. I am not saying "dont pivot", i am just saying you can move your hips without moving your foot. Personally, I almost always pivot to some degree on most of my punches, though that degree varys with the situation i'm in.
Yes, and no. If you want to use a left hook to stop an opponent from moving to his right in order to then create an angle to attack, then no. Pivoting in that situation will slightly slow down your next move. But generally, yes - there's no way to leverage that punch with your legs and core if you don't pivot.