The use of LATH strips to create walls and barriers has been used for centuries. in fact, did you know that wood Lath strips were used as the underlying structure for plaster or stucco walls until the introduction of sheet rock panels in the early 1900's.
Some have said that the horizontal lines and sharp, clean corners are the elements that define the LATH style wood fence as todays MODERN fence style. I'm not sure about that, but as generation X continues to deliver Rat Rods, Tattoo Sleeves, and Labradoodle dogs, why not.
I believe that folks desire the Lath style wood fencing because the design is simple, a little unrefined, and reminiscent of our Cajun heritage.