Why? All a minimum wage does is prevent people from taking jobs that would otherwise go to automated systems. If someone wants to work for $5/hr, who am I to say that's wrong?
The real concern here, I think, is that the minimum wage isn't enough to sustain an individual or a family. The solution there isn't to raise the minimum wage, but to ensure everyone has enough, regardless of wage. So hand out cash so everyone has enough, and then let people work for whatever price they want. Cash handouts should only go to citizens or permanent residents IMO, but everyone is free to compete for whatever wage they feel is fair, and wealthy people can pay the difference.