Always well expressed, Paul Constant.
A concern about dictating a minimum wage is that it's a bit clumsy and that there are perhaps better ways to up people's lives. Paying directly into folk's pockets (including those not working) using some kind of UBI system has the advantage of less interference with the labor market. Although you argue well that there are no problems, there can be down the road. I think of rent control which Bernie has advocated with good intentions -- but, the outcomes on record have not been all together desirable.
That said raising the minimum wage can be an interim fix which can be rolled into something more comprehensive later.
I invite you to read "Wings to Fly -- a Platform for All" here on MEDIUM.