The AASHTO sign spec. doesn't have prescribed limits; it's based on the design and fatigue stresses of the pole at the hole location. If the cross section is reduced enough to push the stresses in the pole wall over the design or fatigue stress limits, the section modulus would need to be increased by adding reinforcement.
I just completed a design for our high mast light towers, which will be 80', with a 24" base diameter, and 8" wide unreinforced handholes. Our pole designs are exclusively controlled by the fatigue stress limits, and the stress limits are considerably higher for unreinforced handholes, so with 8" wide holes on an approximately 22" diameter pole (at the handhole location), the fatigue stress ratio (stress limit / applied stress) was considerably better with the handhole unreinforced.
Rod Smith, P.E., The artist formerly known as HotRod10