Bottomline: when scarcity is an issue, an unregulated free market will inevitably lead to a lack of competition, and thus price fixing.
I see this fallacy all the time. People see economies of scale, and because they increase efficiency to a point, assume that they continue to increase efficiency
indefinitely. The natural result of that train of thought is that economies of scale, left alone, will result in monopolies for everything. Yet, we don't see evidence for this in the real world. Standard Oil, the poster child for this kind of thinking, had,
at it's peak, only 88% of the refining market. By the time the regulation came through, they were down to 61%. How to explain this?
Well, the simple answer is that this line of thought is
wrong. A slightly more detailed answer would be:
Companies that take advantage of economies of scale often run into problems of bureaucracy; these factors interact to produce an "ideal" size for a company, at which the company's average cost of production is minimized. If that ideal size is large enough to supply the whole market, then that market is a natural monopoly.

Very few things result in this natural monopoly, because the markets are so large. Notice, as well, that the curve turns up at some point. This is due to
diseconomies of scale. The market doesn't need your regulations. It's self-regulating.