That's the bottom line - and why, without a minimum wage, employers will nearly always pay less than a living wage. Because if they don't, then the customers will go to Wal-Mart, who will always pay the minimum wages they are legally obligated to pay. (We have an example of this just above.)
That's the problem. And minimum wage works, sorta, to solve that problem; it mandates a 'fairer' (i.e. closer to livable) wage. And since it's a law, then Wal-Mart and Target and Costco can't get around it by cutting wages (and thus becoming more competitive.) That way the store that lowballs its employees is not rewarded by the marketplace.
But at best that's a stopgap solution. Because as time goes on, and the world globalizes, people are moving from Walmart to Amazon to Alibaba - and there's no way any American, ever, is going to compete with Chinese wages.
So a minimum wage hike is necessary in the short term, if only to keep much of America out of bankruptcy. But it's solving the wrong problem. There is a much larger problem of the growing divide between the poor and the rich. We now have poor in this country who will never get out of debt, and we have rich who need never work again because their investments make them $100K (or much more) a year. Year after year, that gap will grow as the rich reinvest that money and continue to accrue capital, while the poor simply get more in debt. (And indeed, much of the reason the rich are getting richer is BECAUSE the poor are going deeper into debt. Witness the subprime mortgage bubble.)
And that problem, in turn, is based on the concept of an ever-growing economy, one that is mathematically unsustainable.
So something very fundamental has to change, and paying poor people a little more is not that change. One thing that can force the change is a collapse of our debt-based economy - but that's a very painful way to change. Another way is something like a move to a central bank for debt (i.e. money) creation but that is sure to be opposed by whatever party doesn't propose it.