Why is a normal vector necessary for STL files?

STL is the most popular 3d model file format for 3d printing. It records triangular surfaces that makes up a 3d shape.

I read the specification the STL file format. It is a rather simple format. Each triangle is represented by 12 float point number. The first 3 define the normal vector, and the next 9 define three vertices. But here's one question. Three vertices are sufficient to define a triangle. The normal vector can be computed by taking the cross product of two vectors (each pointing from a vertex to another).

I know that a normal vector can be useful in rendering, and by including a normal vector, the program doesn't have to compute the normal vectors every time it loads the same model. But I wonder what would happen if the creation software include wrong normal vectors on purpose? Would it produce wrong results in the rendering software?

On the other hand, 3 vertices says everything about a triangle. Include normal vectors will allow logical conflicts in the information and increase the size of file by 33%. Normal vectors can be computed by the rendering software under reasonable amount of time if necessary. So why should the format include it? The format was created in 1987 for stereolithographic 3D printing. Was computing normal vectors to costly to computers back then?

I read in a thread that Autodesk Meshmixer would disregard the normal vector and graph triangles according to the vertices. Providing wrong normal vector doesn't seem to change the result. Why do Stereolithography (.STL) files require each triangle to have a normal vector?