My take on NMW is a moral rather than purely economic one. I feel any able bodied person working 40 hours a week in any job should be able to survive without government handouts.
The economics are mixed, this is a nice overview of the states:
NPR Choice page
I think ultimately, giving money to poor people always leads to more economic benefits than giving it to rich people. You can only consume so much, while there’s still need at the bottom, there’s economic activity that can produce wealth for others at a greater rate than investments or savings.