Think about this... If you pay the private police X dollars (doesn't have to be huge amount as they should have many customers) then they get X dollars. Your money went right where you wanted to. You could likely even negotiate and contractually agree on what X should be. If you don't like it there likely would be competitors.

OR

You can give the government X dollars. They can take a percentage off of that for the politicians to pass the bills and such. So now let's be nice and say that is only 5%... So we are now at Y=X-5%.

They send it to the agency they created to do this policing. They pay a lot of people sitting around desks (some who are looking at porn while at work) so let's knock another 5% off to pay them. Again that is being nice.

Y=X-5%-5% Y=X-10%

The police force must be outfitted. This is likely done through a contractor other than that police force, and NOT chosen by the police force so likely going through a similar bureaucracy as the above process. Let's shave another 10% off there for repeating the bureaucracy.

Y=X-10%-10% Y=X-20%

So being nice... If you want the government to do it your money would be 20% less effective if I am being nice.

Recent studies have shown in reality in many cases the amount of money for grants and welfare and other thing is actually only about 20% what was actually paid. So if you want to waste money... have the government do it...

That is what I was trying to get at in this much more simplified post:

https://steemit.com/politics/@dwinblood/who-will-build-the-roads-answer-if-you-get-out-of-our-way-we-will