> No one wants to hire them at a high minimum wage, especially when locals are readily available
The main drawback to a minimum wage is that it artificially increases the cost of labor, to the point where it's no longer worth it to an employer to hire a low-output employee. I think we'd all agree that increasing employment is a good goal, but an increased minimum wage actually hinders progress on that front. As the minimum wage increases, robots and other non-human investments start to look much, much more attractive. Many businesses would be happy to hire workers for less than minimum wage, but legally cannot, and so do not hire.
Of course, it's a complicated issue. Look at the employment of those with disabilities like Down Syndrome [0], for example. Are these employees worth hiring at $7.50/hour? No, for the most part, they're not. Are some? Sure, but on average there's no way. But are they worth hiring at $2.00/hour? Yes, and they and their families are willing for them to work at that wage, because there are huge benefits to being productively employed.
Recently these programs are coming "under attack" in various states. New Hampshire just made this practice illegal, for example [1]. We'll see how it plays out -- my bet is that a) few news outlets will follow up in a few years and see how many of these disabled workers are able to find new employment, and b) few disabled workers will be able to do so.
[0] http://www.witf.org/news/2014/07/thousands-of-disabled-worke...
[1] http://www.care2.com/causes/new-hampshire-bans-subminimum-wa...