It doesn't require a lot of time, and they aren't doing it in high school classes. 
Once they learn how to write cursively, they save time later in their note writing because cursive is faster.
I transferred from an East Coast school to a West Coast school in the middle of the second grade. The West Coast students had already learned how to write in cursive but I hadn't even started. The teacher didn't want to hold things up, so she gave me the cursive writing text book and told me to learn on my own time. Which I did. It didn't take up too much time.
The most time-consuming part of learning how to write was filling the ink pens and cleaning up the mess afterwards. 
Yes, we had wooden desks with inkwell holes in them for our little bottles of ink. We also had to bring fountain pens and blotter cards to school for our penmanship class. It was really messy for the poor lefties.
I don't recall us falling behind scholastically just because we took penmanship training.
