The public health benefit: Since fast foods are harmful higher prices will discourage people from eating them.
Smaller welfare state: People who make more money will qualify for fewer social welfare programs. We net taxpayers will save money. The Gray Lady's article actually mentioned this benefit.
The immigration benefit: The average skill level of immigrants will go up when the supply of low skilled jobs suitable for low skilled immigrants gets radically curtailed by high prices.
The innovation benefit: High prices for labor are a great incentive for innovation. Look at what manufacturing unions did to boost investments in equipment that raises productivity.
Cheaper restaurants in the long run: The automation of food preparation will ultimately lead to cheaper restaurants (so, yes, the public health benefit will be transitory).When I was in college, I used to unctuously argue that red state governments should ditch the trickle down argument and instead capitulate, admitting they are unable--and their constituents unwilling--to give the poor and downtrodden the legs up they need. Instead, they should use the meager funds they were squandering on such attempts to transport their impoverished populations to blue states where they could be more adequately coddled. It's how someone with a distinctly middle class background morally postures while simultaneously trying to demonstrate independent thought, which I naively thought at the time was something the college atmosphere was actually designed to foster. It made for decent undergraduate discussions at a state university, anyway!
Randall's support for the minimum wage is a variant on that thinking, and unlike urging red states to gift wrap their huddled masses and ship them to the coasts, his idea is practicable. Randall mentions some other western states that allow for ballot initiatives like California does. In addition to the golden state, he mentions Arizona, Oregon, and, worst of all, Colorado. If he had his way, lots more terminally poor immigrants would find low cost-of-living Kansas a reasonable destination. Zip it, Randy!
Contemporary political alignments in the US are such that there isn't one party that backs a bunch of policies that all have the real-world consequences of increasing (or decreasing) the total levels of human capital in the locales that adopt them, or at least not clearly so (ie, the left's support for environmental and other zoning restrictions on commercial and residential construction on one hand and its support for affirmative action hiring practices on the other, etc).
High minimum wages discourage illegal immigration because they negate the the major advantage illegals offer. If slavery still existed as an institution in the US, a mandated minimum wage would, principally, similarly damage it. What it didn't wipe out, it would at least push it underground. Indeed, an almost certain consequence of Ron Unz' initiative, if passed, will be an expansion in the size of the cash (or, more aptly referred to, underground) economy. It's an example of a putatively leftist cause that has the effect of increasing human capital.
Welfare benefits, on the other hand, encourage illegal immigration. This is still one of the biggest issues the left pushes (and the mainstream right opposes) and it has an effect on human capital opposite of what hiking the minimum wage has.
The traditional right needs to get behind artificially pushing up the wage floor while maintaining opposition to increases in social spending. A state that adopted this seemingly 'contradictory' set of policy initiatives, especially one with a large illegal immigrant population (Arizona being the most plausible trailblazer, as it has a heroic recent history when it comes to combating foreign settlement within its borders) could really see an exodus in illegal immigrants from said state as a consequence.