Right, I feel like the name cursive is the problem.
As far as I understand "cursive" is generally the term for any joined up writing. The cursive classes that seem to have traumatised a generation of Americans seems to be teaching a specific and overly extravagant alphabet that is more akin to calligraphy. I would definitely agree that calligraphy should be under an art banner and not a requirement.
I think kids should be taught to join up their writing. That's what happens in the UK and it is used for exams and such up until university.