Seems like the end result of welding the points is the same as twisting one larger plane at the middle. 

Wrong!  You might think that, but I tried it, and it's not the same.  Maybe luxxeon could elaborate on the why better than I can, but I'm guessing it's because the twist modifier is twisting the object uniformly along a central axis (whichever you pick).  You can move the center point wherever you like, but then the twist won't be uniform anymore.  WELDING the two mid points together (ie. collapsing them) happens at the MIDPOINT of the two vertices, which is NOT necessarily the center point of the object itself in world space... in fact, it definitely isn't.  So doing the merge on the vertices like that results in a slightly different shape than simply applying a twist modifier.  Sure, you could go back in after applying a twist modifier and move points where you want them, but then that's going to be just as much, if not MORESO, than just welding them like lux did in the video. Correct me if I'm wrong, lux, but I tried what Sinner suggested, and it did NOT work.

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Tools :  3dsmax 2015, Daz Studio 4.6, PoserPro 2012, Blender v2.74

System: Pentium QuadCore i7, under Win 8, GeForce GTX 780 / 2GB GPU.