Keeping the heel firmly planted on the sole of the boot, and weighting that heel so the tail of the ski is engaged with the snow, is important. That was the thing I was able to start learning after figuring out that I was skiing on the balls of my feet. Keeping the entire ski engaged, tip to tail, is important.
Any time a skier complains that their heel is moving sideways in the boot, there's something wrong with the boot fit. The heel cup is too wide.
If the heels lift in the boot, maybe the skier is skiing on the balls of the feet, or maybe not. But in either event there is too much room over the instep and/or in front of the ankle. That is an important fit issue that needs to be addressed. A lower volume boot may be needed.
In other words, the shell width-wise and volume-wise needs to match the foot's anatomy close enough to keep the heel from loosely wobbling around in there.
King Grump skis with his boots unbuckled. And he keeps his heel planted firmly on the boot sole. His boot shells fit tightly enough to not wobble around his feet when the buckles are undone. And he skis with excellent technique in deep and steep bumps, so clearly his unbuckled boots don't allow his heels to move around in there.
Most people would benefit from having boots that match their feet in 3 dimensions as well as his do.