Having participated in both the argument and the limited use of the tool over time, I've come down on the wood chisel shape and sharpening. That design gives the operator much more control of the result to the extent a man with a developed skill can with regularity split off shingles nearly similar to the ones produced by a shingle cutting mill, flat on one side and tapered on the other.
Am I sure the origin of the tool was one or the other, absolutely not. The original was most likely a superior field method to make shingles faster, nothing more or less, and it probably evolved from there. Like many old tools nobody thought to leave a note for we of future generations to read and learn from.