I've seen this kind of wall built with 12" thick expanded polystyrene foam rather than extruded polystyrene foam (Styrofoam) with joints glued together and with vertical holes for rebar and grout also at the joints. I suspect Styrofoam would be much more expensive.

Our last home had an acrylic stucco over styrofoam exterior, no personal experience about it on fencing. Although, I have seen it. We liked it as you could choose several textures and any paint color on a paint deck, instead of the limited options of regular stucco and it was extremely easy to repair.