The minimum wage should be as it says. It should be the minimum wage. It's enough to avoid exploitation and give the worker a basic standard of living, but nothing else. Anything more and you start getting into that territory where businesses don't want to employ as many people any longer.
Look at France as an example. They have a huge minimum wage. Combine this with workers who spend most of their working lives on strike and you get businesses leaving. It's part of the reason why their economy is so terrible. Why would a business want a French worker when they can pay a German or British worker far less for the same job?
High minimum wages look great on paper, but if it's too high you hurt businesses and the people who then either lose their jobs or who end up not getting a job.