I don't have much knowledge of the laws regarding unions, but I believe there are certain types of jobs that requires Union Labor only. Again I am not sure, but lets say construction for example. Any large scale public works project must be completed by union laborers (at least in NYC), like the new Yankee Stadium or MetLife Stadium. I think some private construction work is the same thing depending on the scale. I also think the public utilities also have to hire union. If this is true, I am not sure how that relationship evolved or how those laws were passed. Another example is the doormen of NYC. Certain large buildings have to hire union doormen. I do not know how they gained this right.
Now retail, and fast food corporations like Walmart or Wendy's is entirely dependent on the minimum wage worker. The CEO, CFO, and HR cannot be at all the locations at once to flip the burgers, cook the fries and take orders. Clothes, sporting goods, canned foods will not stock themselves. And last I heard, we don't have robot security guards (ala Elysium) yet, so I doubt you can trust the customers to check themselves out and pay unless there is actually workers in the stores. I know I wouldn't LOLZ.
Are these minimum wage workers unionized? If not, why not? Unionize, and but pull whatever strings are needed so they have exclusive rights for all the kind of minimum wage work done for these kinds of big box, and national fast food chains. Sure maybe the companies will raise their prices, if they have to pay these union workers more, but lets see how long they can sustain that. Eventually, if they want to beat out competitors, they will have to price compete with each other. Either they lower their prices to be competitive even with higher wages, or they go out of business.
