"Living wage" is a meaningless term.
Offering LESS money than minimum wage is not going to enable any of the poor to dig out of their hole.
By my math, $5/hour is better than $0/hour.
He can't 'compete' because nobody WANTS him to compete. Nobody WANTS to see the guy with the ugly shoes and badly fitting suit in their office.
Again, you're negating your own argument. In your scenario where the poor guy is so repellent that nobody will hire him at any wage, then he's screwed regardless of the minimum wage. In the more likely case where he does actually have some value, he still can't get hired if that value is less than the minimum wage.