It's typically only the heavily processed versions of beans and meats that are cheap. Besides, those items hardly make for a healthy diet by themselves. It's all the other ingredients required that drive the costs up.
Also, your suggestion of simply pushing for cooking classes regardless of the cost, would ironically make the problem worse. The burden of that cost will inevitably land on poorer people. And at the same time potentially removing access to other valuable classes and skills. They will be paying for an education that they still can't afford to utilize.