Actually, the "government as legitimate monopoly on force" meme is only as old as Machiavelli.
https://mises.org/document/1092/Myth-of-National-Defense-The-Essays-on-the-Theory-and-History-of-Security-Production

Now, as to monopolies, I think the definition provided (A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity) is a good one. The article further points out: "Monopolies can be established by a government, form naturally, or form by integration." I'd say the latter two are just versions of the same thing: Market forces make it more efficient for one company to provide that commodity. In a free market, the former one would not be possible. So we're just left with "natural" monopolies to worry about.

Given the particular commodity that we're talking about (money), a natural monopoly is possible, but not something to worry about. For the only way that a provider of money, in the free market, can become the sole provider of money, is to provide the best, most stable, most reliable money. The moment it stops doing that, it opens itself up for competition, and that competition will be fierce.