Everyone over about 40 or 45 had tried to find a job in those hard times. And it's from that group that the policymakers come, not from 20 year olds.
I don't suppose the Kennedys were much affected, but do you really think that Johnson or Nixon, Humphrey or Wallace could have forgotten a decade of their formative years? Even today, those born in the teens, twenties, and thirties haven't forgotten the Depression.
Vietnam is further away in time from us than the Depression was from Kennedy's America. Is it forgotten? Perhaps vivid personal memories have faded, but that doesn't prevent Vietnam -- or WWII or the Great Depression or even the Civil War or Revolution -- from still having a major effect on people's understanding.
If you doubt that people's memories run back a quarter century, start telling people you think Jimmy Carter would make a good President, and see what their reaction is.