This exact kasaha had been bothering me for years.
(I did not expect it to find it asked on a web site).
Here is the pshat that we finally worked out last Sukkos.
It seems that there 2 types of lavud, one that “fills up” the empty space (Ritva Sukah 16b) and a second one that “pulls” the 2 sides together (Magen Avraham siman 632 s”k 5).
The nafkah minah between the two types is if the halachic width of the wall after lavud includes the empty space or not.
The din of lavud by Mechitzas is of the first type while the general din of lavud is the second type.
The general din of lavud is therefore insufficient to give a Sukkah wall a shiur of 7 tefachim because it just pulls the sides together.
So we need the special din of lavud by Mechitzas to give the wall the full shiur which it can because it fills up the space.
Sam2: Lavud is used to pattur hotzaa on shabbos under 3 tefachim (Shabbos Daf 80).