It is not cheaper. The poverty tax is in knowledge, and it is paid twice - easily accessible food is expensive for its quality. With enough money to buy time or expertise to manage your diet, you can pay less money for higher quality food.
The poor don't have time for that or much cooking—they have two jobs.
They could cook on the weekend or on their day off and try to use a crock pot or bake things as those can be done while doing other things at the same time.