How right you are! I remember back many moons ago to how shocked I was when my mother (RIP) pointed out that until the mid-1950's or so that quiting school at 16("dropping out") was no more tramatic than dropping out out out of college today. Many, many jobs did not require a HS diploma, e.g. pump jocky, waitress, barber, clerk, hair dresser, construction work, military, factory work, etc.
Girls dropped out about as often as boys, esp. in rural areas. As my mother said: "A girl grows up to be a farmer's wife. What does a farmer's wife (or a farmer) need to know about French literature?"
My mother, who was born and raised in a small Illinois farming community, hated being a farmer's daughter and was determined never, ever to end up a farmer's wife. When she graduated in the mid-1940's she was 1 of only 4 girls in the entire graduating class of 50.