Narrow road bars hold a few advantages. Of minor gain is less material, arguably lighter weight.

However a large gain could be considered in lowering the frontal area, a more tucked in aero advantage. Wide bars make more of a parachute. Follow the principal of aero bars but also the old clip on super narrow drops. You will see obvious gains in speed.

Then again, they might not help in opening up the chest or breathing, or other issues during climbs. I've read and been told the standard is to find a bar width just under shoulder width. I say use whatever is comfortable.