Your math is correct and I think you pretty much summed up the situation as the breaking up of a monopoly. Force is an industry. Violence is the raw ore, and in theory the government is supposed to refine that ore into a useful alloy, by separating out good violence from bad. Everyone has a financial interest in making sure someone is on guard to physically shut down the robber or the crazy person. The government monopolized this industry by the same logic they monopolize anything else. "This is too complicated for the private sector to handle, this is a fundamental need that everyone should be paying for collectively," and so on.

Until the government mismanages it badly enough, or neglects it from lack of funding, that everyone is ends up having to pay for it themselves anyway. So in the same way that households have to set up a personal generator when the government's electric grid goes down, they will also have to work out a method of replacing the police department and the army. What that looks like in 2100 is surely an improvement over today's system. But as far as 2030 United States goes, it's not looking good. My optimistic take is that there will still be some region within North America that is predominantly English-speaking.