The main problem with your argument is that you're completely ignoring how detrimental it would be to the poor. Private security aren't paid to protect anything other than the specific area that they are hired for, and any private entity will prioritize their own interests and that of their shareholders over the interests of the general public.
What about those that can't afford to hire private security to protect their neighborhood? Singapore has the second highest GDP per capita of any country in the world, it's really not comparable.
We've seen and time again that privatization leads to exploitation. What about the people who live in remote areas with no coverage? Or those with only one option, do you really think they will be offered a fair rate when it's obviously a micro monopoly?
What about those who can't afford to purchase private security?, which is that any system in which people are paying for a service is going to be