I agree that minimum wages are too low but the argument that wages should track productivity is false from economical point of view, in my opinion.
The argument would be true if how people contribute to economy did not change.
But over time disparity in contribution to economy changed. Hundred years ago people had very similar jobs, mostly physical, manual, where each would contribute rather similarly.
Nowadays companies can produce virtual goods, sell "IP", and many other mechanisms to produce a lot with relatively little that just are not possible with traditional production lines.
Now, I think the correct reason to justify better minimum wage is basic human decency and also the role of the state as servants to entire population.
I think a person doing honest, important work for 8 hours a day 5 days a week should enjoy a compensation that should be enough for a basic living plus some little extra. Basic living means a decent place to live, medical care, ability to buy healthy, non-extravagant food, etc.
It doesn't matter if that job is cleaning streets or being cashier at Walmart. We need streets to be cleaned and we need to buy stuff.
These people doing basic jobs are unable to defend themselves and that's where the state should come in and make sure that people who do basic jobs are able to afford basic living.