Total household income. It is possible to accept a lower wage job if the rest of the family is making more. A spouse or older child can add to the family budget even if the primary breadwinner is making more.
Grants / subsidized housing of some sort. College students making a few extra dollars while living in the dorms where the major expenses are paid elsewhere.
Back to the older children and summer jobs. Getting a job to do something over the summer and get a bit of spending money of their own.
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Yes, lower paying jobs within higher cost of living areas are going to be having trouble finding people to work there. This has been a thing for many years. Even in the before times, there were constantly places that had "help wanted" signs out and were paying minimum wage. The ones in higher cost areas of the city were more likely to close resulting in more expensive restraints that can be supported by the people who are living the higher cost of living.
No. Restaurants will continue to exist. Sit down in particular. In cases where you are paying for an experience; the economics will get worse, but they will continue to exist.
Fast food restaurants will even continue to exist. But the latter only with substantial automation. This has already happened at the front of the house -- kiosks and apps are the "happy path" ordering interfaces at every McD's in a major city. I'm merely projecting that the most cost-sensitive segment of the food services industry will push that automation into the kitchen, the checkout line, and a lot of the administrative work that happens at branches.