While your logic seems like it is going in the correct direction in general, I see you didn’t start the chain of thought far enough back. IF you are correct in saying, 
“More crime = more policing. More policing = more shoot-outs, more arrests, more convictions, and higher sentences FOR REPEAT OFFENDERS”
Then you must also admit that:

LESS laws and LAW ENFORCEMENT = Less crime = less policing = less shoot-outs, arrests, etc.

Seeing as how those in power have impunity (impunity means the ability to do something a being too big and important in the scheme of things to be punished) then the responsibility for fixing the situation lies with those in POWER with IMPUNITY. Cops can murder and have impunity because they receive at MOST a paid suspension and they cannot be retaliated against. We cannot fire them, we cannot take their weapons permanently, we cannot fight back in self defense, they can do whatever they want and they have a legal defense since the mid-70s. FURTHERMORE when a cop does this and penalties are paid out to victims those payments come from US, tax payers, not the one that made the mistake.

Politicians and celebrities and pro ball players also seem to have this special impunity don’t they? You know who has NO impunity? Black citizens in America, that’s who. Get an education from somewhere NOT the South, and preferably outside America if you know what is healthy for your brain’s evolution.