Additionally expecting whoever is reading the paper to comprehend everyone's (likely very sloppy, in this era) handwriting is an exercise in frustration for the person who would be evaluating the papers.
Not that tests/exams can't be given on paper, ever (multiple choice still works), but for something where people are expected to provide multiple pages of coherently written essay output, I would struggle to do it by hand. And I'm old enough that we did do a lot purely on paper when I was in school.