We all know that price controls are the worst of policies (look at Venezuela), (begin sarcasm) except when it comes to wages (end sarcasm). Few people would defend price contols except when it comes to minimum wages.
Wage subsidies are better than minimum wage laws, and this is part most people miss, probably at less or the same cost. If you think about the money needs to come from somewhere and the underground economy need to be policed which is a similar cost to dead weight loss of taxation.
But politicians like minimum wage laws because if the voter does not think about it for a minute, it seems free to him. So how corrupt are the politicians who either know better or are purposefully ignorant?
The system selects for corruption.