I have often pondered that whole fall line to fall line approach of referencing turn phases. I actually use it when I'm performing white pass drills or demos because it lets me stay balanced on one ski for one complete turn cycle as defined that way. Overall I feel like I am smoother in my normal skiing when I think of a turn as being on the left edges or the right edges. Turn starts when I engage the edge and finishes when I disengage the edge.
I guess for me I intuitively like the engagement of something that is to be held for the turn duration and then disengaged. In the case of white pass turns, my mental focus is on the engagement of balance on the one ski. The turn starts when I establish that balance and ends when i transfer balance to the other ski...thus its fall line to fall line. In the case of normal turns the balance transfer is not neccessarily that well defined, though its almost certainly generally closer being skis flat to skis flat.
But I think whatever works for someone, this is just mental model stuff. right?