I imagine that the simple geometry of the bowling pin really allows the texture to define the intricacies of how it looks. However, wouldn't we also need to rely on more complex geometry for more organic objects, such as rocks? I think that while from a distance a simple texture might emulate the look quite well, from closer up it might be much less convincing, especially if we are examining from multiple angles.
examining from multiple angles? Simultaneously? You must mean just rotating the objects orientation. Why would rotating the object degrade a texture? Textures are designed to cover the entire object.
I agree that looking closer will break the illusion that texturing provides, given that texturing is supposed to emulate features that one normally does get very close to, e.g. scratches on the bowling pin.