You are right my numbers don't take into account that many of those $15 an hour jobs don't come with paid sick leave, paid vacation, or often, paid health insurance. That does not invalidate the conclusion. The numbers are for comparison. A two income two person household does not need child care.
I don't believe that workers are responsible for the rise in productivity, I believe productivity increased due to automation and process improvements provided by capital investments. Why would the fruits of that investment be reflected in wage increases. Wages should increase when workers provide more valve not when automation makes workers jobs easier or require less skill or education.
TEK