Now, I know that there are many companies that force people to be on with a live video feed, and that many don't really like it.

How about recording a 3-min clip and playing that in an infinite loop - creating a fake feed (remember Keanu Reeves' Speed?) - so that people can avoid not being seen, but still get things done better? A mask on the face is a simple addition to avoid detection. As the saying goes, modern problems require modern solutions!