I don't think the point of drawing the weapon is early enough either.
When I hear the testimony in many of the questionable cases, I get the impression that the officers have charged in and escalated the situation to the point that is becomes violent and dangerous. That is behavior that we should capture and use to uncover the needed improvements in public safety.
There are disciplines, such as psychiatric care, that deal with agitated and violent people routinely, where lethal force is simply not an option. People in those positions usually have training in verbal deescalation and non-lethal containment techniques that reduce the chance of injury to both sides. There are a lot of things that can be resolved simply by dropping the "I'm a bad ass and you must obey" attitude. It isn't about abandoning the authority of the position, it is about exploiting normal human behavior to your advantage. And, it isn't a matter of years of professional training, either. Nurse's aids with GEDs are trained in the basics in a couple of hours.
If you are trained to resolve a situation with an unarmed individual by using lethal force, there is a problem with the training. Until we fix that, people will continue to die needlessly, on and off camera.