You think that will occur in isolation and no other reaction will occur ? If so you are quite ill informed of the basic laws of economics.
First if you want more of something, you lower the price. You wish to have less of something you raise the price. A fundamental law of economics.
A minimum wage of $ 15 in most (but not all) states would be more than a 50% increase. This will not happen in isolation and the results will be measurable quickly and the result will be less minimum wage employees. Let’s take flipping burgers as an example. At 1st people will just choose to let employees go so you will have less people flipping burgers.
However other folks will start to come up with machines that will replace an entire classification of workers, like flipping burgers. There are companies right now that are building production prototypes of machines that will make a burger to order.
Perhaps the $15 amount that is advocated here will be the tipping point so burger chains start to order them in a few places. The first ones most likely will break down often, and not work quite right. However the learning curve will bring about better machines and quick. Eventually the cost curve will reach the point when it will be the choice of all burger places to buy the better burger flipper, or what ever it will be called.
So in 7 to 8 years all of a sudden there will be no human burger flippers.
I know it sounds compassionate, but the result will be the opposite of what you intend.