There are approximately 46 million people receiving food assistance of some sort. Not only would delivering boxes of food create difficulties in differentiating families with different needs, but it would require a gigantic logistical effort.
The USPS delivers ~200 billion pieces of mail annually, but it does not differentiate between letters and packages. I believe it is safe to assume that the large majority of deliveries are letters. With 365 daily deliveries of food through the USPS we would be shipping an extra 16.5 billion, relatively heavy packages through the system each year. This will create an enormous extra burden on the USPS, requiring significant investments in new facilities, extra postal workers, and extra equipment.
Not to mention we have to deal with what happens if a package is lost (family goes hungry?), what to do about people with food allergies, etc, etc. This is an absolutely terrible idea.