Mitchell, increasing the minimum wage is not the greatest way to put money in people's pockets. Much better to do that directly and not tied to work.
The disparity of income is a huge concern that is damaging in the ways you point out. It's ultimately detrimental to everyone, including the very wealthy.
It can be fixed not by taxing the hell out of the rich but by freeing up the engines of our prosperity -- the big three being innovation, trade, and immigration. This exchanged for an economic platform from which all have a shot at achieving their aspirations.
Key to this is a revision of work and particularly JOBS. They are currently at the center of people's lives and lock everyone in. Jobs (as such) can disappear because they do not drive the economy: productivity does.
Blaming the rich is fruitless; they are no more greedy or heartless than you or me. Leadership, a willing public, and good legislation can make the necessary changes.
Many thanks.
I wrote, "Please, Joe, Not Another Term" and invite you to read.