No, I am not asserting that.
I think the first thing to clear up is our definitions. My main point would be that a market that is controlled by a monopoly is not a free market. I would define a free market not as a market that is free from government interference, but a market in which all of the actors are free to participate on a fair competitive playing field.
I think that lassaiz-faire, with the meaning of "hands off" may be a more precise way to describe what you are saying when you say "free market".
I think that a fair competitive landscape is ultimately what we want out of markets. I agree that it is bad when government actions interfere with a fair competitive landscape. But it is not inevitable that all goverment actions will do that, and in many cases government action can help rather than hurt. And similarly, plenty of actions by non-government actors can interfere with a fair competitive landscape as well.
In other words, the thing you are talking about _does not exist_ except in libertarian fantasies. Without a government (the monopoly on force in a region, that controls the markets within) providing the backbone for this - i.e. with features such as courts, police, mint - there is no freedom, because an aggrieved party has no recourse other than violence.
I think it comes down to the category of item being offered in the market. Some things naturally lend themselves to monopolies; it feels like perhaps it's based on factors like the difficulty of entering the market with a new product at all, the amount of coordination and manpower required to field it, and the cost efficiencies of having a singular producer vs. many.
There are certainly cases where we see duopolies or triopolies etc. where one really-well-run company might be more efficient, from a labour standpoint; but then, in turn, we all benefit from having a redundant array of supply chains.
There are other cases where we absolutely want a monopoly, such as with policing, or (in many countries) with healthcare, because they apply to everyone and being a consumer of the service is not exactly optional.