If the box is subdivided, then you don't need to achieve the effect Bevelled cube is perfect example why you should take the area into account, because that's a straight example from real world artists use on models to make the lighting look better. If you wouldn't take the area into account you would have to add extra edges on polys next to bevelled edge to get expected result.
You'll need that anyway, even if you take triangle area into account. Basically you want the vertex normals of the side polygons to be the exactly same as the face normal.
It seems to me that you are confused what vertex smoothing tries to achieve. It tries to approximate a curved surface with lighting. Now, it doesn't make sense to approximate a box as a curved surface since it's not a curved surface, unless you are cheap in modelling a sphere (: That's why artists have options to define where the smoothing happens with smoothing groups/angles.
Suppose you have an approximation of a sphere. Now imagine that you take a small group of polys and replace them with a single larger one. The vertex normals shouldn't change, it's still representing the same sphere. However, not only has the larger poly a normal that is further away from the original vertex normal, it also contributes more because you take poly area into account. So, in a way, for equal results, you should be using a weight that is inversely proportional to area.
The bevel of a box is indeed a good example. It shows that as an artist adds more detail, the normals of that detail should be more important, since it more closely approximates the reality. Thus again arguing for a normal weight that is inversely proportional to area.