Minimum wage is a jobs program for the rich.
Employers want to hire the best candidate available. Low pay means low-skilled job applicants. The lower the pay, the fewer expectations hiring managers have for applicants. If a job were to pay $6.25 an hour, the person hiring would expect the least attractive applicants, non-highschool graduates, ex-cons, etc. Force employers to pay more and the applicant pool fills with more attractive candidates, highschool graduates with references and no criminal record. Obviously the company is going to hire the most skilled and most trustworthy employee available. The non-highschool graduates and the ex-cons just got priced out of the market, same with the immigrants and all the other people who would gladly have some level of income versus nothing.
There are government credits and tax benefits for companies that hire ex-cons and other low desirability job seekers, but that's just another case of government creating the problem then "fixing" it with tax dollars. It all ends up being a whole lot of waste. But that's government for you.