Basically what you are doing with that argument, is you are saying that if a little of something is good, a whole lot of it must be better. Things don't work that way.
If I got home from work, and discovered that the temp in my house is 16 degrees, I would be foolish to turn up my thermostat to 120 degrees. There is a range for everything that is optimal.
We don't know exactly what this optimal range for minimum wage is, but we can make a pretty good guess. At the low end, it could be anything over $0/hr, so let's call it a penny. At the high end, it's mathematically impossible for the minimum to exceed the mean average, and the mean average amount of value produced per work hour in the US is around $60. But if we set the high end of this range at $60/hr, then everyone would make the same wage, regardless of productivity - that's a mathematical fact. There are obviously reasons why some people should be paid more than others, I think we can all agree on that. Thus, the high end of the range which contains the economic optimizing min wage can't be $60/hr. Maybe half that amount, probably more like a quarter of that amount (in the neighborhood of $15-$30/hr).