The most important lesson for the Police is this: the police officer in charge of managing an incident must be hands-off. They need to be able to do command & control with an objective perspective. As soon as Derek Chauvin was hands-on with a suspect then the protocol should have had him designated on the specific as subordinate to any of the officers there not hands-on. Commanders need to have enough distance between themselves and the action to make good judgment calls.
Good theory. Of course, in this case there may not have been time or space for such while surrounded by a noisy, excited, seemingly hostile crowd of "civilians".