I'm totally going to sound like a Right Winger for part of this, so fair warning:
One way or the other you're going to be paying people a living wage. Whether its by mandating a livable minimum wage or by making up the difference in welfare payments to those who aren't getting paid enough. That or you let people slowly die through insufficient nutrition / medical care / housing (which I'll admit is a more popular solution than I'd have anticipated).
Setting a minimum wage below living and then making up the difference in welfare is effectively subsidizing company wages out of the public pocket. Why should companies who can't afford to run themselves be living off the public largess ?
I get the appeal of this as political rhetoric, but the economic justification seems pretty obvious to me.
Basically it's just "too high of a minimum wage causes unemployment", right? Plausibly there are people who it does not make sense to employ at a living wage* (this is obviously the case for some disabled people, but plausibly it's true or will soon be true for a significant part of the population). If your minimum wage is set at a living wage, these people don't get employed. They then need to be provided with 100% of the equivalent of a living wage through welfare (or they die in the streets). Meanwhile they're not doing much useful labor. This is inefficient, since their labor is worth
something. Better to employ them at less than a living wage so that society
only has to make up the difference rather than providing 100% support.
I guess it's the difference between looking at low minimum wage + EITC as a subsidy to companies employing minimum wage labor and looking at the EITC as a jobs program for people who aren't employable at a living wage. The jobs program works less well when a specific employee's employer has to make up the entire gap between market wage and living wage - they have a lot less reason to keep the person employed. Maybe in some cases the balance of bargaining power is such that many minimum wage employees really could be paid much more without that impacting companies' employment calculus, but there's no a priori reason to think that the living wage level is related to the marginal product of low-skill workers. It seems to me that what you want** is to set the minimum wage to their marginal product and then, if that's lower than a living wage, make up the difference with EITC.
*Probably in the real world it's not that specific people either are or are not employable at some wage but rather that there will be some number of jobs at different minimum wages, but I don't think that changes much.
**If what you want is economic efficiency. At some point we should be thinking about whether someone's labor is worth sufficiently little to society that social welfare is maximized by not trying to make them work so hard but by giving them more leisure time.