In the perpetual struggle between attractive symmetrical handrail bracket layout and safe
robust attachment to solid wall studs there are only two real alternatives:
1. Preinstalled wall cleat reinforcements between the studs at the handrail location
before wallboard is attached or
2. A surface mounted decorative backboard securely fastened to available wall studs
however they are spaced.
In most homes, the only practical balance between the two opposite requirements is
the surface mounted backboard firmly attached to every wall stud with brackets located
as needed evenly spaced the length of the handrail.
In this picture from the Wayback Archives handrails run up each side of the stairwell.
The backboard is ordinary stock pine outlined with cove moulding and fastened to
each individual wall stud with countersunk screws. The brackets are spaced evenly
along the length of the backboard as needed.
Of course, a backboard is not necessary if the placement of handrail brackets
eclectically follow the wall stud pattern without regard to symmetry.