The reality is that if the minimum wage had stayed consistent with productivity and inflation since 1968, America’s lowest earners would be making around $24 an hour by now, an analysis by Jacobin found last year. Fifteen dollars is not asking for a lot. In fact, it’s asking for less than the bare minimum of what we should be providing our workers.
When productivity increased, minimum wage earners do make more.
Overall productivity increases don't increase profits. They reduce prices! Workers make more because everything costs less.
If you increased minimum wage with productivity, it would eclipse the highest earners in a matter of decades. It makes no sense to do that.