hm, being 'more efficient' would be true if the ideal way was known.
Waterfall would also be 'more efficient' if we knew the right product to make and way to make it. If agile has taught us anything it's that we don't know and we can't know. We learn through trial and error and continually innovate. If there is only one company there is no incentive to innovate and discover better efficiencies.
So while the 'logic' is right, the supposition[0] is incorrect.
This is why 'the market' is the best way in practice. We observe an ebb and flow of centralization (Amazon is a good example) and decentralization in various industries. This is caused by innovation and disruption. When one company innovates/disrupts so well and continues to execute it can become a de facto "monopoly," gaining near 100% market share.
When the industry and market are allowed to continue unabated[1] this 'monopoly' can eventually be broken if the company fails to innovate and leaves the industry vulnerable to upstart disruptors. The very possibility means even with 100% market share the company is not a true monopoly, and in practice the consumer benefits from the company's 'existential fear' which motivates it to continue to serve its customers in better and better ways.
[0] knowing the best way
[1] assuming the major player(s) doesn't lobby/enact regulations to protect its market/industry position
edited footnote formatting