The doff and don is not approved by any agency I know because of the danger of embolism.The only weight belt drop exercise was in my Basic NASDS/YMCA class and it was the old ‘Doff and Don’ exercise in a 10’ pool. I was new…It took me a couple times. The lady who was to become my bride however did the entire exercise without a hitch…she was a ‘fish’ like some SB descriptions. Too long a story to pass along. But it really shouldn’t be a requirement. As you have pointed out a chance of drowning or embolism. A ‘Real’ danger when diving.
In 2007, Allison Rainey Gibson, a scuba instructor had students at the University of Alabama doing that exercise, and one of them died of an embolism. Here is an initial description of the event. Google her name and you will see details of the criminal charges she faced and the wrongful death lawsuit that was filed. I did not see any articles detailing the aftermath of those legal actions.
Years ago one of my instructors did an unannounced, unofficial exercise to see how I would react in an emergency. I did OK. He later did it on another student, who did not do OK and very nearly created a double fatality.