In my opinion, the problem with policing in America can be reduced to a few broad things:
1. Police wildly overestimate the amount of danger they're in. Yes, they are in a front-facing profession and yes, any encounter can turn deadly for them. However, from 1980 to 1998, the FBI estimates about 64 felonious police deaths a year for a national police force of 80,000. The stress of being constantly alert for danger is taking untold effects on their collective psyche in ways that are not good for their interactions with suspected lawbreakers.
2. Since at least the Clinton administration, there has been an insane push to militarize our police. This includes selling directly to states and municipalities an entire arsenal from assault vehicles to heavy weapons to armor. It includes training centers around the US for police to learn military-style breaching, containment, and other tactical skills. It includes the rise of SWAT teams (most of whose time is spent collecting parole violators). Police are trained and then equipped to deal with an "enemy" and not their own public.
3. The lack of mental health and child safety workers put police in the position to deal with issues for which they are untrained and unprepared. There is a way to contain an outburst by an adult with autism. There is a way to confront a disrespectful child in a classroom. Neither requires body slamming them.
3. Systemic racism in employment, housing, and schooling has led to a disproportionate percentage of people of color living in poverty, living close together in apartments or tenements, getting sick more often, and having a greater percentage of unemployed teenagers. This greatly increases the opportunities and incentives for crime. Heck, it greatly increases opportunities for arguments, spousal abuse, alcoholism, drug abuse, and just plain neighborly fights. If the disproportionate number of lawbreakers that police see are minorities, police (being humans) will associate being a minority with lawbreaking.
I speak of "police" in broad terms. I am sure that some police officers will never engage in inappropriate behaviors. I am sure that nearly all police officers want to be effective public servants and believe they are being such. I am sure that nearly all police officers go through nearly all of their days without using excessive or unwarranted violence. It is, in my opinion, a difficult and noble profession. I think that we, as a republic, have let them down.
The above problems are difficult but necessary to fix. Above all, we need a massive push to educate all students, to integrate low-income housing into higher-income areas, to train a new generation to succeed in the job market and to participate in the economy of the nation. This will take, if we start right now, about twenty-five years. We need to demilitarize the police and give them more nonlethal options. We need to spend the funds to create functioning juvenile justice, mental health, and addiction systems that can identify problem behaviors before they become criminals.
But that would be difficult and require thought and effort. So, basically it won't ever happen.