Areas of Detroit have more access to protection through
private means than public. Some have neither. But that's not an indictment against private industry. The fact that
private options exist in spaces where public protection doesn't is evidence that a private means of production is again more efficient and effective than the public's.
Both systems fail to protect everyone, and also fail to provide everyone with justice. The only question is which mitigates the amount of people without, and by extension which provides the most people with.... therefore making your god of the gaps question "What about Xe in Y and Z position" a silly question to begin with. You're giving the pass on the obvious problems with the alternative means of production.
Even more fundamentally, we acknowledge that we wouldn't want government producing out cars or TVs. Security and Law are at least as difficult to produce as cars and TVs so why would we demand the government produce and distribute them as well?