I don't think wood running boards were ever -specifically- banned.
All running boards on new house cars ended in 1966 and were eventually
mandated to be removed from all cars that did not require roof access
(like cars with roof hatches). The most recent photo I have view of a car
with a wood running board is a 1974 shot of NP 27306, built by ACF in 1941.
The car was repainted in NP's billboard paint with the 96" herald but the
wood running board remained in place!

Tim O'Connor