Good point. An instructor at an SSI shop (where my daughter was certified) once told me that it was strictly forbidden. He lead me to believe it was an agency policy, but it could very well just have been his policy. Reason cited was just as you said, it's a distraction.I don't believe any instructor would want you filming new/discover divers while they're doing skills as you'd be a distraction. For the same reason most don't allow cameras on those dives. So that may not be as profitable as you'd expect.
However, filming seems to be a regular part of more advanced classes. I recall Harry Averill filming my first day of Cave1. Presumably so they could laugh over beers or something . Harry wasn't teaching the class.