We actually did this but not an entire episode. When I used to do song of the day it was one we did and I told the story but a full episode or may be a Prof CJ segment is a good idea.

The song likely most associated with 60s anti Vietnam protests has zero to do with Vietnam and never did nor anything to do with war or foreign policy.

Just like most people think the show Mash was about Vietnam. Americans are not just ignorant of history but their own very recent history.