Earlier quoted context omitted.
I agree that one needs both and that they serve complementary purposes. But a minimum wage is useful to the extent that there are jobs for your lowest skill, least desirable workers. And ensuring that may take reducing the work week.
Higher minimum wage laws do hurt low skilled workers. We have two great big machines at work each will pay for it's self in under a year at current minimum wage rates. There is no choice but to replace the people for machines if we want to remain competitive.
Self checkout came regardless of whether the state had a minimum wage increase or not. As soon as the technology was mature enough it was rolled out.