You're still thinking in the box. What's a sidewalk? A place owned by government. Almost of this kind of crime takes place in "public" places.
So we ban sidewalks -- and other "public" places -- and almost all murders will cease?
How often are people "found dead" in shopping malls? Almost never. Unlike governments, private citizens take care of their property. What's more, if it did happen, you can be damned sure that the owners would want to get the perp. This kind of thing could be bad for business, don't you know?
Three points:
1. Are you seriously suggesting that violent crimes "almost never" occur on private property? I would like to see some data to support this.
2. Why would the owners of a shopping mall necessarily be interested in pursuing the murderer of a stranger? True, a dead body can be bad for business. But if it the victim were not a family member, friend, or customer, the property owners could avoid bad press by simply disposing of the body quietly.
3. Suppose the owners of the shopping mall did decide to pursue the murderer. How much would it cost them to hire their own private investigator to do the job?
No, I am not. But mystery murders almost always involved public property to one degree or another.
Why would the owners of a shopping mall necessarily be interested in pursuing the murderer of a stranger?
Aside from the possibility that their actions might be discovered, malls want to be safe and pleasant places for their customers. This is a sign of serious problems, is it not?
Suppose the owners of the shopping mall did decide to pursue the murderer. How much would it cost them to hire their own private investigator to do the job?
Far less than it costs to get the police to do the same thing. Police are bureaucrats who spend almost all their time writing down what happened. Like all bureaucrats, they work inefficiently and stupidly. I was recently arrested on a trumped-up assault charge (later dropped). It would have been laughable to see the amount of useless activity, except for the detail that they were doing it to me.
I would also assume that mall owners would have insurance against this kind of thing, as a matter of course. Which would spread the cost around among all mall owners.