They can say that, but that doesn't make it true.There is no way the government can possibly determine the market value that a given employee brings to a business because that's not a one-size-fits-all answer.It is in the interest of employers to keep wage costs down, consequently they tend to pay as little as possible regardless of what they can afford or the market value being produced by their employees. Human nature 101. Therefore the need for an independent arbiter - the government - to set a minimum wage.
Thus your argument is inherently wrong.
Apparently it can, and it has worked. We have had minimum wage and conditions for many decades:
"The Australian Federal Minimum Wage has long historical roots going back to the 1907 Harvester Decision which established a 'fair and reasonable' wage to meet the needs of a working man and his family."
Basically all methods of driving up wages are ways of reducing the labor pool. Someone has to lose.