Writing an essay by hand in the exam room is also the norm for a final exam.† The term used at my high school was "in-class essay", and they weren't rare. At no point did anyone feel the need to use paper that was bound. Paper is paper.

(I can't really speak to college; I didn't take classes that required essays.)

I always loved in-class essays as an alternative to take-home essays, since the demand on your time is zero instead of "lots".

† A final paper, in contrast, would be written in advance. Usual practice would be to have the paper and the exam. Is the article really saying "schools have started giving exams again"?