I don't have a strong position either way on exactly what the best minimum wage is, but I think it's clear that there are people who have skills and abilities in line with creating maybe $10, $12, or $15 per hour of value for a business. If you make it illegal for an employer to employ them at a rate where it's profitable, you're either forcing them to be out of work, to accept a quiltwork of hours ("we will only employ you for 2 hours at lunch and 3 hours of dinner rush"), to be in a precarious situation at work, or to find an employer willing to dress charity up in work clothes and lose money by employing them. I don't know how common it is, but I'm quite certain that I know people (in the sense that I can name them) who fall into that category.

I think substantial increases in the minimum wages force those people into a lottery where some are made better off and others are made worse off, but where the ones made worse off are made much worse off (out of work, higher barrier than today to finding work, everyone around them has more money and everything is more expensive than today).