Great article, Steve.
Problems are best dealt with when they appear one-dimensional. When it's obvious that "Bob" did it and look no further. But the problem with police brutality is layered - it's institutional, it's the training (or lack of it), it's allowing bullies in Blue to exacerbate the problem - it's all over the place and rightfully so because we are a complex society with NO one-size-fits-all solution.
Police are sent out to arrest the bad guys, mollify upset domestic partners, babysit kids on their own, sort out traffic violations, hunt for terrorists, deal with the homeless, and if they get any of this wrong - all of them take a hit on their credibility and usefulness.
Society - which means all of us - needs to get better and more layered in handling our problems. Different people with different training for different problems.
Police brutality has the same root causes as spousal abuse - it's the character of the person, their mental state that drives them to violence. They don't belong on the force.
We can fix this. But as you say, not by getting constantly distracted by what is not the problem.