Personal opinion here and I will probably get hate mail for it. The minimum wage should be zero.
My first reason: having a low paid job (basically an internship) while in college allowed me to show some experience and allowed me to get my first paid job.
Having this option would be even more important for someone with only a high school degree or someone that wants to go from one type of employment to another.
Somehow we think it is great for people to give money for education, but exchanging their time for real working knowledge is rejected.
Second: It limits the variables that people can agree to work for. A lot of people would love to work a couple days a week with out pay for health insurance. Others might like to work for a month for free to get an understanding of what a job field is like. I though for years I wanted to work in the food industry. I fortunately had the opportunity to help out a friend in a catering business and realized it not a career choice for me.
Third and probably most important. I believe it hurts the least employable people. They are the first to lose their jobs, replaced by people pulled into the labor pool by the hire wages.
Looking forward to constructive comments