The problem I've always seen with minimum wage not being a living wage is this. If people can't make enough to live on, then what little money they do have will only be spent on necessities, and the cheapest ones at that. How can any business survive if people can't actually afford to buy your crap? Now if everyone makes at least enough to live on, and still have a little money left over, then they will spend that, your business will have more customers, more income which offset the slight increase in salaries.
I put a lot of blame for the wage gap on the Regan tax cuts. Before income over a certain point were heavily taxes, so if the company owners wanted to avoid paying those taxes they would reinvest a good portion of the money back into the business, for expansion, upgrades, employing more people, paying them better. When those tax cuts went through and the owners could pocket a bigger portion of the profits, well then increasing profits became priority. And the biggest expense was labor, so fire people, make those left take on the extra work, and make sure no one is paid what they are worth.