I understand what your trying to accomplish with this alternate perspective,,, you're using it as a mental tool for smoothing transitions. I fully support the concept if limited to the context of an exercise used for that specific purpose. But I balk at the idea of changing the long held concept of where a turn truly begins and ends.
Reason 1: Falline to falline is just plain wrong.
When skis are tipped onto their right side edges they begin to turn right, when tipped on their left edges they begin to turn left. When they are untipped (returned to flat) they stop turning and the turn comes to an immediate end. These points at which actual turning begins and ends are the logical locations to designate as the beginning and end of a single turn. Students quickly grasp this concept because it's simple and it jives with their prior experiences and thoughts on turning.
Reason 2: It's really two turns.
Falline to falline is really two turns. One to the left and one to the right.
Reason 3: It ain't about the falline.
In the traditional concept of the beginning and end of a turn the falline doesn't play much of a role. In real skiing edge engagement and release are not necessarily tied to the falline, they can occur at many different orientations to the falline. Viewing the start of a turn as simply the rolling of the ski onto edge, and the finish as the return to flat, allows for all those variables.
Even in the falline to falline philosophy the S turns described can, in real skiing, occur so that the apex of the turn is not in the falline. In fact, turns can be made in such a manner that the transition between left and right edge engagements (the traditional beginning and end of a turn) can occur in the falline, bringing the transition and the end of the turn (according to the falline to falline philosophy) into unity, the very thing this new concept is trying to avoid.
Reason 4: It creates new problems.
While the falline to falline philosophy may serve to attract focus away from the transition in the hopes of smoothing it, it's dulling focus on a portion of the sequence that contains some very crucial skill areas.
There are multiple types of turn transitions that need to be learned and refined if a skier is to advance to upper ability levels. This cannot be accomplished by treating transitions as a non event. They MUST be focused on.
Same with turn initiations. Progressive edge engagement is a skill that evades the masses. To refine sensitivity and feel for the edge the student must key his focus into the moment in the turn where it begins,,, the transition.
These skills don't just magically develop with no direct attention being placed upon them,,,, yet distracting attention from the very moment when these skills are executed is what the falline to falline philosophy strives to do.
So, as I said, while I do see how using the concept as an exercise to achieve a specific purpose could prove very effective, I see many pitfalls in the idea of completely supplanting the traditional edge engagement to edge release theory with it.