Please cite your source where the minimum wage was only meant to be a "starter" wage. Oh, wait you can't because that's capitalist propaganda, not the actual truth. Here's the actual reasoning behind the minimum wage: to maintain a "minimum standard of living necessary for health, efficiency and general well-being, without substantially curtailing employment."

If the wage can't pay for the "minimum standard of living" like rent, utilities, and groceries, it's not doing what it was created to do and must be raised.