This has more to do with the lift leg opening early, than the natural tendency to turn on the ball of the back foot.
The two issues that you expressed above are seperate disciplines, apart and not in connection with one another.
The pivot foot is a platform base, a stability issue that has very little movement other than to provide a foundation for building and progessing everything topside (upward only.) It is not affected by, nor is it "caused" to do anything the pitcher doesn't want it to - deliberately. If a pitcher concntrates on keeping the pivot foot down , so be it, it will stay down and collasping on the instep is a deliberate, mindufull act. Regardless if the leg lift is high, medium, or low. Also, regardless if the hips are open or not.
Try it yourself and you'll notice the sperate focual point of your pivot foot's control rests with your delberate concentration on that part of your body - regardless of what the rest of you is doing.
The leg lift is a different matter and does not contribute downward or any where near it (base). The leg lift is an upward only progession that dictates hip, pelvic, trunk and shoulder platforms and how these parts of the body move - based on the pitchers's natural and trained endowments.
Players with large trunks and girth, have a tendency to open early due to the extra bulk their carrying, unless skillfully trained to do otherwise. Also, the same is true with pitchers that are exceptionally tall and slim. Their posture after a leg lift can be even brittle at times.
In any event, The two ... pivot foot and leg lift are not homgenous to a pitchers cause and effects. Each can and without the other, move and function seperately without major impacts to the other. Again due to the directional influences of each ... the pivot foot is purely a static stability issue down and in place , the leg lift is a fluid posture issue with upward dynamic influences.
On the other hand, each by themselves can have a cause and affect relationship like opening too soon, landing off to one side or the other, and so forth. For instance, a pitcher can have excellent pivot foot discipline, but the leg lift discipline is so flawed that all kinds of control and other topics start to float to the surface.
Deep stuff for the middle of the week.