I think it is really funny that you consider cleaning to be an unskilled job and cooking to be skilled job. They are both low skilled job that are a lot of work. Your anecdotal "they like being a cook" misses the point. On the margin, some people will choose cleaning over cooking.
Society agreeing on a minimum wage does not make it efficient by definition. First of all, "society" is only the majority of voters. Voters pass things that are inefficient all the time. Secondly, efficient has a specific meaning in economics. It means that goods are allocated to where they are most highly valued and produced where they are can be most cheaply made. Given the definition, the minimum wage clearly does distort people incentives to work and leads to economic inefficiency.
Society agreeing on a minimum wage does not make it efficient by definition. First of all, "society" is only the majority of voters. Voters pass things that are inefficient all the time. Secondly, efficient has a specific meaning in economics. It means that goods are allocated to where they are most highly valued and produced where they are can be most cheaply made. Given the definition, the minimum wage clearly does distort people incentives to work and leads to economic inefficiency.