One of the demands at the March on Washington was for a $2 minimum wage, which would be $15.27 an hour adjusted for inflation today. But later in life, Martin Luther King Jr. endorsed a different idea—a guaranteed basic income—which as I've said before is the real smart solution to the low-wage dilemma.
The minimum wage typically gets debated in terms of econometric studies about disemployment impacts. But the problem with the minimum wage isn't the alleged disemployment, it's the freedom. Imagine a worker earning just slightly above the minimum wage, and also working under some kind of conditions that he finds annoying. He goes to the boss and asks for a change. Turn the heat up a little in the winter. Or let him pick which music plays rather than sticking with some dumb playlist that's been assigned from the top down. Or get a more comfortable chair. Or manage the line this way rather than that one. There are dozens and dozens of little non-wage decisions in any given workplace that impact a person's happiness and life satisfaction. But the manager looks at it and says there are sound business reasons for sticking with the status quo. Now the problem with the minimum wage is that even if the worker values the change much more highly than he values an extra 2 cents an hour, he's not allowed to trade 2 cents an hour for an improvement in his working conditions.
Conversely, I strongly suspect that one reason empirical studies often don't show disemployment effects of minimum wage hikes is that there are a lot of non-wage dimensions to the employer-employee relationship along which things can change.
The problem with no minimum wage, however, is that the kind of freedom involved in allowing for unconstrained wage bargaining is that "the law, in its majestic equality, forbids the rich as well as the poor to sleep under bridges, to beg in the streets, and to steal bread." The ideal solution to these problems, however, lies not in the workplace but outside of it. Exactly where King and Henry George thought it belonged—in guaranteeing to everyone a minimum standard of living whether or not they work. With that in place, employers will face a de facto minimum job quality. Your job has to beat "unemployment + living off the GBI" rather than "unemployment + homelessness." You can reach that job quality threshold with money. Or you can reach it by providing valuable training and experience for the future. Or by having a really enjoyable atmosphere of some kind. Realistically, it'll be a mix.
Now obviously you can say "guaranteed basic income," but that leaves the question of how high the guaranteed basic income should or could be. That's a matter for another day.