The problem with minimum wage is that there is no minimum wage guarantee by the state. The same problem applies to price controls of any kind. If nobody is willing to sell you a product that satisfies the price controls then you go home empty handed. If the rules are too strict and end up preventing the market from working then the government is to blame and the government has to step in and actually provide whatever nonsensical guarantee it made.

If the government wants to prevent you from getting a job that pays less than minimum wage it has to provide you with a job that actually does pay minimum wage.