Because individuals at that level of income have little leverage and are willing to work for what enough people see as unfair compensation.
For example, I would consider working at fast food joint HARDER work than my own, even though it pays only a fraction of what I make. Minimum wage helps to even out a bit common compensaiton disparity like that.
Your employer does not pay you by how hard you work. Your employer pays you based on your skill and how much money you make for the company.
Your wages are determined by how much your employer can get somebody else to do the same job at the same quality of work that you do.
For instance you take a job as a fast food worker. You are doing a job that requires minutes of training which means anybody can do it. You may be working your ass off, but your employer can find dozens of people to do the same thing.
Not so if you're an engineer or a registered nurse. That requires years of training and even more years of experience. You can't find dozens of engineers or ten registered nurses on your street. Because of that, you are worth more money to your employer.
And? The point is minimum wage laws step in where pure market creates a desparity too great.
Minimum wages laws don't solve that problem. If they did, then 2009 should have been a utopia.
Total fact and logic fail.
Fact: Minimum wage was nationally most generous in REAL terms in 1960s and it's been shrinking ever since.
Logic: Just because a policy reduces economic disparieties
does not mean it fully solves them or creates a utopia.
Nor do we even want them to be
fully solved because while we want to moderate some of the excesses of free markets, fundamentally supply and demand dynamics are still the main drive of our quite successful economy.
Second, there is not one single example in all human history, where the increasing the minimum wage did NOT cause unemployment. There is nothing 'generous' about putting people out of work.
Third, there is nothing about the minimum wage that reduces income disparities, because the minimum wage, regardless of what the law says, is always zero.
Not a single person came on after the minimum wage hike of 1996, or the minimum wage hike of 2007-2009, and said "Look disparities have decreased!"
My point is, the minimum wage does nothing that you claim it does. It does not 'moderate some excesses', nor does it reduce disparity, nor is it 'generous'. There isn't a single aspect of the minimum wage that is good, and plenty that are bad.