How many security firms do you want to choose from? Five? Let's say five. So to equal the density of a municipal police force, that would mean five times as many officers employed at those security firms. That's five times as many officers being paid.
Wanna try making sense? If you replaced the current police force with 5 private agencies, that doesn't mean there are five times as many officers. What kind of dumbass logic is that?!?!
It just means that each firm will be one fifth the size of the former monopoly. People aren't going to change careers just because there are more companies to choose from.
So you want a security firm that has only one fifth the number of feet on the ground than what has presumably been determined to be an adequate number? Assuming the same coverage, they will have one fifth the density. Due to the random nature of crime, there will be times when your call for help will result in a much longer response time than occurs now. There's no way around it.
From a logical point of view, all you need to do is take the notion to the extreme to see the problem.
First of all, just because a publicly funded police force has a certain number of cops, does not imply that that number is optimum. Second, in every city that I've lived in there were always the city cops, the county sherriffs (and contables), the state cops and the city cops of the surrounding suburban cities. All of these different units communicated fine and seemed to manage the distribution of workload without significant problems. There is no reason to assume that several private security units working in an overlapping geographical area couldn't manage to do the same. The 911 operators generally have to choose which unit to call, and have radios that can switch frequencies to do exactly that (or call the different units' own dispatchers to do it).