From what I understand, the problem is not minimum wages, but unstable employment. You may be getting paid an acceptable amount but at the drop of a hat your employer will say that you aren't working next week which is much harder to cope with than earning less but knowing you will have x in the bank every week.
Big cities still need people to do the jobs that only pay minimum wage. There was a whole thing last year about how important those minimum wage workers are, but you've probably forgotten already.
Never stated that they weren't important? Most minimum wage workers I know that work in the city live outside of it.