The body will always strive (and win) to be balanced, otherwise we fall. If the hips (specifically back hip) fires / rotates just prior to front foot strike, the shoulders will stay back...otherwise the body will be out of balance. Hip rotation prior to shoulder rotation is the ONLY action that will create hip to shoulder separation. Hip to shoulder separation has been surmised to account for up to 80+% of velocity....separation / distance of the back hip from the throwing arm / elbow creates the stored elastic energy (stretched rubber band) ultimately in the arm layback position that creates velocity. Arm action at or inside of 90 degrees at the high cock position aids in this as well.
Edit to add: if you can get the pitcher to learn how to activate the hips prior to FFS, the hip to shoulder separation (keeping shoulders back) becomes a "non-teach" it happens automatically....and to a large degree this is true of arm action. What happens first, directly affects what happens next. Too many instructors teach the symptom, without realizing the cause...this creates IMO - robotic, non-athletic pitchers that all look the same.
I've not had quite as easy a time. Comparing most major leaguers to most high school pitchers and what you'll find is that, while they are able to keep the shoulders back, it's at the expense of full rotation of the hips by foot strike. Part of it is conventional instruction which teaches that you need to hold the hip rotation back as long as possible and fire the hips around. these instructors find some value in the velocity of hip rotation. The first faukt they will try to teach out of a kid is "hurdling." I, personally don't find hurdling to be any big problem. And, while late, quick hip rotation may help some pitchers achieve separation, I don't think it's necessary to achieve it. That particular velocity I don't think is a necessary part of the kinetic chain and the energy produced is bled out at foot strike anyway. I teach my pitchers to try and get the hips open early. It makes it more likely that they get there by foot strike. As long as the hips are fully open and the upper body has not yet began internal rotation (but has completed external rotation), you are exactly where yo want to be.
I look at it like this. If you are shooting a rock from a slingshot and you pull it back six inches really fast is that going to provide more velocity to the shot than if you pulled it back six inches slowly? No. the tension is the same between the handle (braced lower body) and the pocket of your slingshot (not yet rotated upper body).