This is a fantastic question. This question asks if abolishing our current monopoly on force (the state) and allowing those functions to be handled voluntarily will open the door for a new monopoly on force (a new state) to form from among those interactions. Before I answer, I want to point out that naturally I think many of the state’s violent functions aren’t fit to exist in the first place. However, there are some functions that are needed—primarily the need for defense against those who would attempt violence on the innocent.
My answer is the standard answer you will get from anyone coming from an individualist anarchist point-of-view: state interference in the marketplace is anti-competitive and therefore facilitates the creation of monopolies in the first place, and they are unlikely to form on their own. We assert that monopolies/large corporations owe their existence to a mutually-beneficial symbiotic relationship with state powers. For example, Benjamin Tucker wrote a piece about the “four monopolies” supported by the state that have led to our current manifestation of the capitalist system: money, land, tariffs, and patents, and also said that “when Warren and Proudhon, in prosecuting their search for justice to labor, came face to face with the obstacle of class monopolies, they saw that these monopolies rested upon Authority, and concluded that the thing to be done was, not to strengthen this Authority and thus make monopoly universal, but to utterly uproot Authority and give full sway to the opposite principle, Liberty, by making competition, the antithesis of monopoly, universal.”
Whether through IP-related laws, subsidies, or legislation that outright bans competitors from offering services under the threat of violence (the case with most government-provided services), government intervention provides various degrees of immunity to competition. Therefore, in absence of this power, I and many others view the marketplace as likely to disperse rather than concentrate, and do not think large monopoly powers in anything will form organically without performing some criminal act to get there. That said, I am not saying it is impossible that a monopoly on force could re-form. I suppose it could happen under unusual circumstances. I could also get struck by lightning three times this week.
Obviously there is a lot to consider here, and more than I can fully address in a short reply. My suggestion if you are truly interested is to take a look at work by individualists. A book that explores the concept of the market as dispersive and also includes a lot of early individualists is Markets Not Capitalism, so that might be a good place to start. This has all been a verbose way of saying that, without a state, I don’t expect a monopoly on defense to form any more than I expect a monopoly on salads to form. Keep in mind, of course, I am answering this question from a largely individualist perspective. If you were to ask a communist this question you would likely get a different answer. Thank you for the great question and I hope you are interested enough to do some reading on this subject.