Note how much higher the unemployment rate is for people who don't have degrees in this graph:
Would unemployment rates be lower for people with low education if their minimum wage was lower than that for, say, high school or college graduates? We would signal to folks that the floor below you on wages is higher as you invest more in your education as well as raise the prospect of lower unemployment rates at every level of education.
People who are chronically unemployed are more likely to be depressed, have financial problems, have bleak prospects because of falling further behind on job skills and promotions, and be unhappy. What if we let more people work?
Separately, we could adjust incomes of these working poor so that they would not only have jobs and better prospects for future gains, but enough income to live a normal life. Even with this, it would be cheaper for us to subsidize their jobs and better for them to work them.