The labor market is not a magical entity. It's comprised of companies doing the hiring and people doing the working.
If you look at sectors where unskilled work prevails and corporations treat workers as fungible resources then the labour market lies firmly in the supply side, and workers have no alternative other than getting exploited. This means paying the least possible amount, which means less than minimum wage.
Think about it for a second: why do you think so many companies pay minimum wage, and not a single cent more? Is is because the workers' negotiating power magically breaks even at the minimum wage level, or is it because labor laws make it illegal to pay less than that?
Also the alternative is having some of those people have zero income and no opportunity to develop skills.
Joshua D. Angrist and Guido W. Imbens “for their methodological contributions to the analysis of causal relationships”
They have done real world studies on the issues discussed here and arrive at a different conclusion from you.
Counterpoint: Bangladesh. The labour market does not choose to work 60hr 7day weeks for $75/mo performing skilled sewing of your clothing because they like it: it is because they are left no choice. Given the opportunity, corporations will just as happily enslave Americans as it does third world citizens. Already does, in fact: slavery is still legal via imprisonment.
Corporations could choose to pay their Bangladeshi labour significantly more, and it would cost you only pennies more for your shirts … but they don’t. They pay as absolutely little as possible. They will inevitably do the same to you.
I don't understand. How is the rest paid?