That even pre-dates the Great Depression, so I wouldn't lay that one squarely at the feet of the Greatest Generation. Methinks that change was driven by the same people who brought us all that one world order stuff in the early portion of the 20th century.
Withholding actually only dates back to the Current Tax Payment Act of 1943.
Before WWII income taxes primarily fell on millionaires. Some government funding still came from tariffs rather than income taxes. The income tax didn’t become widespread until the 1943 act was passed.