The essence of free markets is competition and this applies equally to wages as to prices. In theory the system is fair, but in practice, a handful of major players set the wage level for smaller competitors as well.
Look, at the end of the day, what policy makers really need to be looking for are ideas that most efficiently reduce wage and income inequality. That's a main reason why I've been so stuck on full employment, as it perfectly meets that criterion.
When opponents talk about who's earning the minimum wage, they're often referring to the demographics of those at today's minimum. But that's not the relevant sample when you're evaluating a proposed increase in the wage floor.