"Pointless rant", maybe not, more clarification might be in order.
It seems like you can do a transition anywhere and you don't need a line to tell you when to do it.
This is correct if you want to do half turns or edge sets or unfinished arc. The idea in teaching is to get everyone to set a base standard for their turns. The base or "Example turn" is one that encompasses all the techniques and virtues you want and need to become an expert skier and one that helps you control speed. There is a time and place for the turns you refer to, but they are not the ones I was referencing when I described where to finish a bullet proof short turn relative to the falline. What I am referring to in my books and video, are the "Example Turn", which is a turn with a "high C" start and low "C" finish. In such turns there is a reference point to when the skis enters the Falline, to begin a release. If you don't care to make round brushed carve, bullet proof short turns, proceed as described in your post.
Hopefully I've got that right. If not please correct me.
Well, if you have it right and it may well be that you do, but it will sure complicate the hell out of skiing, which is already complicated enough. If I am confused by your point, there are probably at least a handful of others in the wings that will be "really" confused.
In this situation the imaginary line dictated by gravity (the fall-line) is replaced by the line down the mountain that represents your direction of travel
This is really confusing, as 99% of the time your direction of travel should not be down the mountain; it should be either toward the side of the trail or back into the trail. You are only directed to the bottom of the mountain for a fraction of a second, when you are actually in the same direction as the Falline.
The line (ninety degrees) off the moving outside ski is a reference that always moves with you. It can always give you a reference for which way your body is facing relative to the outside of the turn. Use this line to aim the pole tip for the no swing pole tap. This does not have to be related to the Falline, however, if you don't finish an arc with a "Lower C" finish into the falline, you won't have a bullet proof short turn or a brushed arc turn. BPST and Brushed Carved turns are the turns where the Falline reference is used. If you want to make edge set turns (no bottom C), use the ninety degree, no swing pole tap reference shown in the videos. Also, in flat terrain, with short carved arcs that are not finished completely into the Falline, to such a high degree as carved arcs on steeper terrain; you can use the ninety degree line off the outside ski for your CA and pole tap reference.