I'm not sure what we are talking about here. Monopoly's on money, or monopoly's in general?
Well, to stay strictly on-topic, we should limit the discussion to monopolies on money. Specifically, the service of providing the commodity that is used as money in a marketplace.
In a free market, I think monopoly's in general will almost certainly develop over things that are scarce. (Car's, food, computers, etc.) This is not a good thing, because it centralizes power.
This is patently and provably false. The computer market is one of the least regulated on the planet. Cars have only safety and emissions regulations to contend with (and many companies voluntarily exceed those regulations). Food, similarly, has only health and safety regulations, and a few labeling requirements. You chose the worst possible examples for natural monopolies, since all of those industries show robust competition, in a largely unregulated (free) market.
Since you can use anything as money though (hence it is not necessarily scarce) I agree with you (Myrkul) on the money part.
Well, at least you can see
some sense.