The purpose of pay is not to make someone work harder, but to incentivize him to work more hours (and to keep him from moving to a competitor, obviously). There is a lot of things people could be doing with their time, and each marginal hour of work has to provide a greater utility than the alternatives.

It's not the market's role to take care of people who are not fit to work. I should note that the main impact of a minimum wage is to create extra people who are now no longer employable.