I suspect this would need to be city-wide, or otherwise regional to make sense from a logistical point of view.

But the most likely criticism is the lack of variety. You send somebody food they don't like. e.g. A meat-eater who doesn't like beef, and they'll be unhappy regardless of how healthy it might be. Suddenly you need to let people choose from a menu, and the economies of scale become harder to achieve as you've got to cook N-types of meal, not two.