“Should this bench have absolutely zero movement,”
Nothing is infinitely rigid.
I have hit the end of my workbench to reproduce what you have done.
It of course react to the blow but any vibration is nearly immediately dampened.
1/16″ is not much. It will of course depend how hard you hit your workbench. (although I don’t see the point of doing that).
I have made my workbench with recycled wood. Not any dimension is exactly what P.S. was proposing as they all were adapted to the material available.
IMO no dimension is critical.
In the blog you mentioned vibration while planing against the grain.
Sharpness is a cure to most problems.
Make also sure that the cutting iron is not rounded at the very tip of it (that might happen while inadequately stropping). If the very tip is rounded there might not be any relief angle anymore. This would require you to push very hard vertically on the plane to get a shaving in the middle of the board. (I say in the middle because the plane will always succeed to byte the board if starting from the edge of it.)