Earlier quoted context omitted.
Strange you don't consider Vietnam a major war. I won't blame you for forgetting Korea though as even contemporaries did so. For me the definition of "major war" is were civilians forcibly conscripted.
Total deaths of the Vietnam War, on all sides, were around 1.5 million. Korea was around 1.2 million. WWII was 50-90 million and WWI was 40 million. Vietnam and Korea (two conflicts that my father actually fought in) were wars, for sure, but not major wars compared to the World Wars.
There's no reasonable way to conclude these were not "major" wars in the context of US history.