Most proponents of raising the minimum wage cite the Card & Krueger paper which has aged quite poorly. It turns out that chain fast food restaurants are a poor proxy for the minimum wage labor market. If you want to know the most up to date data backed perspective on the minimum wage, look to the Seattle minimum wage study.[0][1] In short, the benefits of raising the minimum wage go to experienced workers at the expense of inexperienced workers.
We know that price controls don't work. Having a minimum wage limits the freedom to negotiate the value of your labor at a rate that you'd be willing to take. Instead of a wage that they are willing to accept you force them to have a wage of zero. I don't believe there are any situations where people are better off when a third party eliminates economic opportunities for them.
The national minimum wage should be zero, as is the case in countries like Iceland, Norway, Sweden, Finland, Denmark, and Singapore. You could also argue that the minimum wage is unconstitutional considering the history of supreme court decisions on the issue.[2]
[0]: https://evans.uw.edu/sites/default/files/webform/w25812_summ...
[1]: https://www.econtalk.org/jacob-vigdor-on-the-seattle-minimum...
[2]: https://en.wikipedia.org/wiki/The_switch_in_time_that_saved_...