You will note I never said all minimum wage workers are school leavers etc. So there are certainly older ones but my main point stands. These workers are better off and the national is better off if they are employed. Simply requiring employers to pay more for minimum wage workers will mean employers will reduce the number of workers thereby further burdening the state and/or disrupting communities with disfunctional and dissolute people.
You will find good arguments for abolishing any sort of minimum wage. I like Milton Friedman. A couple of quotes.
“Every economist knows that minimum wages either do nothing or cause inflation and unemployment. That’s not a statement, it’s a definition.”
“The real tragedy of minimum wage laws is that they are supported by well-meaning groups who want to reduce poverty. But the people who are hurt most by higher minimums are the most poverty stricken.”