I can't find a good reason for this anywhere. The reflection vector used in phong has a simple basis in physics. But the half vector used in blinn seemingly has no rational basis, and does not constitute a proper reflection. And yet it is used in every so-called "physically based" shading function. If there is a good physical basis for it, I'd like to know.
What I've been able to find are a few reasons:
It's faster - there's mixed information on this, but even so it would have been a great reason... in the year 1998.
It handles angles higher than 90 degrees better - as far as I can tell the only reason for this is because the phong term has been used improperly. The dot product of the reflection and the view gives an angle between -1 and +1. Usually this angle is clamped to 0 to 1, this is the direct cause of the 90 degree problem. Re-normalize the angle instead of clamping it and you get the full 180 degree coverage. I refuse to believe a simple x * 0.5 + 0.5 operation has eluded the graphics world for 40 years.
it handles edges better - The edge "problem" also exists in the blinn solution, just to a lesser degree. The main cause is improper simulation of area lighting at the terminator, which should be essential for any "physically based" shader. But even in simpler situations a sigmoid function can approximate a soft terminator line correctly. Multiplying into a lambert term is incorrect as it attenuates the specular term improperly, this could cancel out a fresnel term and lead to further errors.
It has long reflections at the edge - It seems to me that while anisotropic reflections may be realistic, blinn is not the correct way to implement them, as they only appear at the edge. It is merely a happy coincidence that an error in the H term happens to look realistic.
None of these reasons are satisfactory, I want to sort out this madness.
I want to clarify that I am not talking about blinn and phong specifically, but instead about the vector components H and R, which are used as the basis for these shaders as well as others.