This may not be the most popular thing to say, but ... Just move? If you are the head of a large household living in an area where the cost of living is too high to support your dependents, you would do a whole lot of good for them and yourself by starting new in some other part of the country. At the very least it would be wise to relocate across the Bay. I realize that people have families, social networks, and sma…
If you're hand-to-mouth poor, you cannot afford a rental truck, let alone time off work and still feed your children. You will probably lose your job if you move, and not find another one where you land, especially if you're in the service industry. Good luck with that East bay -> peninsula commute on your minimum wage. The reason many cannot get jobs other places is due to felonies or other legal issues related to being poor.
If your children are in school a lot of parents would actually rather struggle than put their family through the trauma of a move, even if in the end it may be better.
American society is more mobile than others, but poverty (outside of vagrancy) is extremely restricting.
I do think your main thesis is correct (this is unmaintainable, gtfo), but moving is a multi-year struggle of planning and saving at these low levels of income.
This is at it's core class struggle, not individual unawareness.