OK, the expert in the video is full of poop on that issue then.
before the Civil War a Cavalry private was earning $8 a month, a sergeant $13. During the war a private was paid $16 but dropped back to $13 for the private after the war.
I guess war really does cause inflation.
source: “US Cavalry on the Plains 1850-90”
Guess getting shot at more often costs more than 50 cents a day + that good Army chow.