I think it's rather telling that you don't think there aren't worthless workers. Worse than worthless, often times those employees simply suck money from the company by distracting good employees. Not all minimum wage employees are in this category, of course some are just *gasp* students/part timers/trainees/whatever but the people who cannot get a position above minimum wage at 7.25 clearly aren't worth 15. There are people who simplydo not careat all about work. Not enough to support themselves or their families, not enough to want to do a good job or even keep one, anything.
For whatever reason you cannot disconnect idealism and reality. You aren't alone, of course, why does Apple pocket unending gobs of money with absurd profits while basically enslaving Asians yet get upheld as a 'progressive' (or at least the chic choice of progressives) company? I don't know. What I do know, though, is all your idealism doesn't solve the simple math problem of how a small business owner with little to no margins goes from paying say $8/hr for an employee to $15/hr without gaining any additional benefit out of them and continues to operate without making serious changes (ie, cutting staff and increasing workload).
I would be absolutely thrilled if the floor for employee value was $15/hr because then I'd get all my chicken sandwiches with chicken on them.