One of the nice things about creating your own shaders is that, as long as you’re not attempting physically based lighting, you can define what looks right to you, and I would encourage everyone to play around with the calculations in the shader. I don’t always use the same strict values, and as you suggest, yours is probably a nicer result here
The Phong shader is not a physically realistic one, and neither is your result. One of the properties of a physically realistic renderer is energy conservation, which means that the energy emitted cannot be greater than the energy received. (see Adopting a physically based shading model | Sébastien Lagarde)
If you are going for physically realistic (PBR), then I would recommend the seminal book which is now available free online: Physically Based Rendering by Matt Pharr, Wenzel Jakob, and Greg Humphreys: http://www.pbr-book.org. Also the more approachable PBR guide from Allegorithmic: The PBR Guide - Part 1 on Substance 3D Tutorials
Your suggestion of the first argument error, I hope to update in the next version of the book. I made a diagram of the cone direction: Chapter 5, cone direction - #2 by caroline. As long as the math is correct, it isn’t an error, but, as you say, could be clearer.