But you seem to be unhappy with the current system of the hundred or more big firms and are advocating disbanding these current governments and switching from this to even smaller firms. I'm confused because I believe this will naturally lead to these firms growing into larger firms with no oversight by the public at large and thus eventually give you even fewer options.
As to what it's called; the extortion would be called a compulsory service fee, war would be called large scale protective operations. What people call it privately isn't a problem until the point at which the extortion is costing them more than they think they can save by revolting.
As to why would the business do this? Because they can make more money doing this and it's not illegal because they are the law. They do not care about the good will of the customer, because the extra cost to the customer is not enough for the customer to act on. Prices are set to what the market will pay, in this case it's as close to revolt as the business can get away with.
I would also like to point out that I don't disagree with your assertion that their are negatives with a government controlled monopoly on law enforcement, I disagree with the idea that a free market system for it would not be subject to worse corruption/abuse.
Well, ask yourself, these days, how many people can you convince that bullying is a good idea? Just because an idea is not something that you would choose if you're enlightened, does not mean that people will not backslide into it.