I've got to disagree with you on this one. Look, my leadership was dog shit when I was court martialed, they basically trusted one misquoted OSI statement and assumed I was guilty for 6 months. But one thing they did well was keep silent publicly. And I wouldn't have expected any sort of public vocalization of support. They had no idea if I was innocent or guilty. You don't back a potential criminal; you quietly provide support to an innocent-until-proven-guilty person until the process is played out.
But when you have a video that shows, at a bare minimum, a very uncertain situation that probably didn't go the way you would hope it would, then you should not be making any statements that imply your subordinate did the right thing. Because how can we trust in the process when one of the people who is a literal avatar for the process, the police chief, is not acting in accordance with the concept of blind Justice?
I don't think a police chief should be fired because one of his guys fucked up, unless and until the process shows a leadership failure. But part of the police chief's job is public relations, and reflexively supporting an officer who, to my eyes, looks to have murdered an innocent man, is a failure of his position.
The tragedy in all of this is that policing very much does need an overhaul in the US, which is an argument from the left. Unfortunately the left has only bad and completely misdiagnosed solutions, whereas the right, I believe as a result of the left's unfair crusade, is reflexively supporting the police to the detriment of potential reforms.