Who am I to tell a homeless person that she is legally forbidden to engage in a voluntary, hourly employment contract for less than $15/hr? I would effectively be guaranteeing that she stays unemployed/homeless. Regardless of practical effects (which are ambiguous at best), it's wrong on moral grounds.
On the other hand, the minimum wage definitely benefits middle class teenagers on their first jobs (if they can get a job), and has questionable benefit for millennial humanities college grads who have yet to start a career. For them, the higher wage comes with fewer hours, according to this study.
In the long run though, the more we raise the minimum wage, the sooner the local price inflation catches up. Getting a casual meal in Seattle is NOT cheap right now.
EDIT: I'll throw in that I think a very basic income with no minimum wage/unemployment/other welfare is much smarter fiscally and economically, and is the only way to largely eliminate extreme poverty. And it's sad that HN readers flagged this article because it challenges a conventional liberal talking point.