While I don't agree with the status quo, if your labor isn't worth $15 an hour to someone (mainly because someone else is perfectly willing to do the work for less) then they don't have a moral obligation to pay you more, and minimum wage laws only artificially constrict the limits of what the value of unskilled labor is.
I'd rather see a basic income guarantee (mainly for creative people like artists or FOSS developers) and the removal of minimum wage, so businesses can correct the true value of labor in various fields.
It would help eliminate the rampant service industry that destroys souls because most people don't have the fortitude to deal with random strangers idiocy.