When you say "we agree" - does that include the people that end up unemployed because the expected value of their work is less than the minimum wage? Whereas had they been allowed to work for less than minimum wage, they would have been able to build a track record of reliability, reducing the risks of hiring them in the future and thus increasing the expected value of their labour?

I would love to see the data, but in my experience of growing up in a very poor neighborhood, getting a foot in the labour market is the difficult part; once you are in, moving up is relatively easier.