Correct. The economic arguments against a minimum wage are correct, but they are also irrelevant.
The Congress, or any agency it may create, has NO Constitutional authority to impose a minimum or maximum wage.
——What an employer pays an employee is no business of the federal government.-—
Actually, by law, what an employer pays workers is set down annually in a form W2 describing precisely how much was paid. The knowledge is necessary to determine exactly the income to be taxed.