Just responding to this part of your post. Part of your argument works, part of it I think leaves out or ignores some important issues. A big part of the issue here is that what most Americans consider an acceptable standard of living (especially in high-cost-of-living areas) is fairly expensive by global standards. You have to consider that the amount of money it takes to live that way may simply be more than the amount of money that 40 hours/week of certain kinds of labor are worth to a rational employer. If a person is not able or willing to do work that pays enough to live in a given city, who should bear the burden of that fact? The employer, or society at large?
If you say the employer, then consider how the employers will respond. As an employer, I might want to have a nice man in my building's elevator to push buttons for guests who are laden with suitcases and small kids, but simply cannot justify paying that man $290 a week ($7.25 x 40 hours). His labor is just not worth it. I could pay him $50 a week, but not $290, and I'm not allowed to pay $50. So I do away with the job altogether, and pretty soon my customers (and everyone else's) get used to it, and so now instead of every building in NYC having one of these guys, only the ritziest hotels in town have one. So now instead of hundreds of guys having a crappy job, only 2 or 3 guys have a job (and it's still crappy). Hundreds of jobs in NYC alone disappear, which reduces opportunities for low-skilled people to learn basic job skills that (hopefully) they can leverage into a better job.
Note I am not suggesting that we expect these people to live or support a family on $50/week. There will always be people who just are not capable, mentally, physically, or both, of doing work that pays enough to live on. Our society needs to face the fact that we have poor people in our midst, stop blaming poverty on the poor, and support the poor with well-designed, easy to navigate safety net programs that don't disappear when they get a low-paying job. At the same time, we have to recognize that when we try to load the whole burden of social safety net programs onto employers, employers are going to react rationally to those increased costs by offshoring, automating, passing on costs to their customers, or just flat out eliminating marginally productive jobs.
ETA: IAppreciateIt's post #147 is saying the same thing I am saying here.