If you're running on the delusion that any relevant percentage of employment agreements in modern times can be considered to be an agreement between equals, sure.
But given that many employers tend to have hundreds/thousands/millions of times greater financial power than any given employee, I fail to see how any sane person can consider that an agreement between equals for the purpose of law.
We do actually have a perfect example of this playing out in modern times, in China (and to a lesser extent India), which gives us a perfect example of what happens in a modern globalized country without minimum wage laws:
China has no minimum wage laws, labor is cheap >
Lots of companies move in to take advantage. Unemployed people are still desperate, so take any job >
As more companies moved in to try to compete against other companies, unemployment dropped to near zero >
What used to be long lines of prospective employees at the company gates, has turned into empty parking ports, with not enough employees >
Companies in China started struggling to find workers, and have started to compete for labor >
High demand for employees + low supply of labor = higher wages and better benefits
End result is, despite the media sensationalizing the destitute working conditions in China because drama sells in TV, the quality of jobs and the average wage in China have shot up dramatically over the last decade. So much so that for many companies it no longer makes sense to outsource to China or India, as they'll just break even on shipping charges. The same thing happened in India, but on a much more dramatic, and possibly unsustainable level. So, here's your example of the "tragedy" of the lack of minimum wage laws in modern times. The market works, and it's not as bad as you think.
(Source: series of case papers from my Global Economic Environment graduate class)