Is it any better than regular log cabin built with just two axes, or even one if you don't need hewing? I see straight timber beams cut with modern mechanized sawmill, a laughingly thin filling of clay and single-glaze windows on your pictures. Maybe something like this would make sense in Africa or where you come from, OP. A carpentry manual from 1850 describes fachwerk structure in following manner: "Buildings of this sort are built for dwelling only in warm country and come in two- or three-floor varieties, in colder country only summer dwellings, warehouses, stables, barns, etc. are erected in this fashion.">>99
You have very strange understanding of what mesoamerican and european medieval architecture looked like. Especially if we talk popular dwelling, not fortresses or places of gathering built with slave labor. The most popular easiest design was semi-underground thatched roof mud hut and it still is in some parts of the world, something less primitive than what OP describes, that thing came after 16th century when river sawmills were become widespread.
I'm not sure what you mean calling symmetric architecture being unable to hold it's weight. On the contrary, all self-supporting structures ought to be symmetric.