In my high school many of the authority figures, and what amounted to the “home room”, were segregated. Also, the rules were different for boys and girls, so it may have been easier for each authority figure to only be handling one set of rules. I graduated in '75.
In my Jr HS (which was quite the notorious hell-hole) both the Boy’s VP and the Girl’s VP administered “swats”. Even back in the days where corporal punishment was though to be OK, many could see the problem with a man giving such punishment to a young nubile underaged girl. (In fact I don’t doubt there’s a number of porn movies have a plot line about that).
I went to thoroughly co-ed public schools, but we had a Dean of Girls & a Dean of Boys.
The girls had to be watched as hemlines began creeping up; you couldn’t have a male teacher keeping his eyes on us that closely. Just before graduation (Class of '66!), Coach Roach refused to give a couple of boys their robes until they went for haircuts…