That only applies in an economy without credit and where sales are constrained by the spending of the wage share. In an economy with credit you can use financialisation to give people spending power their wages don't permit, which keeps prices higher than they would otherwise be and allows more to flow to the profit share.
The dynamics then drives the path of interest rates down over the years until you get a credit crunch - at which point the lack of spending from the profit share suddenly shows up in a Minsky Moment.
There's an inductive connection between the monetary economy and the real economy, not a direct one. It works more like an iPhone charger than a 1 bar electric fire, and that means you need greater monetary 'apparent power' to get the maximum level of real economy 'true power'.
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.