Plus, let’s face it, it’s exhausting. I know faculty that are constantly monitoring for cheating. And they hate it. It’s wasted effort.
Teachers should monitor students, but for learning not for cheating. By assuming that students are learning, or trying to learn, they will engage more effectively and they will also know when students aren't really "doing their own work", and know enough about that to move the student to more productive activity. Not only is policing a waste of time, it corrupts the learning process and pits teacher and student against one another.