1. When more than 2 positions are set with the Line Renderer, the thickness of the line attenuates to invisible at the end of each section. Because of this, the Line Renderer cannot be used to depict a network of beams - something it should be ideal for.

2. Example contains a 2 position Line Renderer, which maintains width while rotating.
You can also see an example of a Line Renderer with more than 2 positions. Note, how the lines between end points diminish until they are invisible - the effect is like long thing triangles, rather than lines.