They leave those areas because of enormous crime and shoplifting.
It must be practically impossible to entice workers for the low-wage positions in a supermarket in an area where NOBODY works; I see posting on indeed.com for those positions all the time. My town (between Newark and Jersey City) has a Wal-Mart that attracts customers (and shoplifters) from both, and it is amazing how nasty the welfarians are to the employees. I couldn’t imagine working that job in THEIR neighborhoods (the “food deserts”).
Newark now has one or two chain supermarkets; most closed when the city fell half a century ago, and there was simply no reason to replace them.