Ok, in the open market, how would anyone even know which one to call when they saw a house in the distance on fire?
There are no monopolies on doctors. How much would you pay for private security in that scenario? what about the people who don't pay, can I take them as slaves?

"There are examples of these working very well in poor areas of Chicago. "

No there aren't, the one that anarchists keep citing is mostly an overpriced firearms training school whose service to the community is mostly to advise the community to call the police. That is not a substitute for the police.

In an open market, there is no possibility of a monopoly.

ROFL