The problem is that if you set a minimum wage that is higher than the real value of the work performed, it means those jobs just simply won't exist anymore.
The real value of a lot of products and services is more adjustable than your statement would lead someone to believe. Reality is absolutely not an efficient marketplace that immediately culls jobs and workers the moment a certain price of labor threshold is reached.
And yet ATMs, self-checkout lines and online shopping are a thing, and so are bank branch closures, retail bankruptcies and mall vacancy rates.
That is efficiency. We won't pay people to dig ditches when we have machines to do it. Efficiency is not the enemy, resource distribution is.
In a world where CEOs can receive massive bonuses for driving a company to the ground, that's not easy to believe at all.
As far as I'm aware, none of the studies on increasing minimum wage have shown this.