I would never use standard framing for outbuildings. They don't need it. 2ft on center is far more than you need for a coop but you still need a nailer every 2ft for the sheathing so it's what I do. Most of the time 2x3 timber is same price as 2x4 so it doesn't matter, if cheaper then I use 2x3's because overbuilding is just more money. The roof should be 16 on center as it holds snow. What's amazing to me is people use 2x6's on short roofs, again, way overbuilt.
16 on center and large timber frame are for residential. The reason, besides convention now uses 16 inch insulation and we want 6 inches deep insulation, is we don't want our finished houses to flex. It pops joints and screw heads on sheetrock and so on. To keep the interior finish looking nice we make stiff buildings. An unfinished outbuilding like shed or barn can flex all they want. It doesn't make the building shorter lifespan. Having timber on ground and not staining or painting exterior does.