With all due respect. In WWII, the average American man was not 5'5" tall as stated by you.
From the early 60's through to 2000 (a 40 year period), the average height for men grew just one inch. The height went from 5'8" to 5'9". You are asking us to believe that in the previous just twenty years (1940's to 60's), the height had grown 3" (three times the amount in half the time) from 5'5" to 5'8".
"Men's average height increased from 5 feet 8 inches in the early 1960s to 5 feet 9 inches in 1999-2002."
USATODAY.com - Americans growing taller and wider
LiveScience.com - Four-Decade Study: Americans Taller, Fatter