But what’s odd about your argument is that the federal minimum wage ought to be $12-13/hour if it had simply been adjusted for inflation since the late 1960s. So by that measure, we value “unskilled” labor even LESS than we did half a century ago.
If we had adjusted minimum wage for productivity growth, it’d be about $21/hour right now.
So I think we ought to have a nationwide federal minimum wage minimum of $12.50-15/hour, adjust it for inflation continually, but also adjust for local cost of living so that the nationwide average (average of regions) minimum wage is around $21/hour, continually adjusted each year for cost of living.
And I am not worried about automation increasing unemployment over the long term. We should have targeted efforts to increase employment rate if there are periods of disemployment from disruptive automation, but we have more jobs now than we did a century or two ago in spite of two centuries of increased automation and mechanization.