If this happens the company that gets the contract might go with USPS but I don't see it for one of the reasons you said.
These will be going to a lot of low income housing, especially large cities. We are taking 60,70,90 % of neighborhoods getting heavy boxes of food, twice a month. With that you are talking 3 to 20 stories building. And even the low income housing (houses) there's usually mail box units that only holds a 8 or 10 inch by 4 inch box.
So this will not be part of every day mail carriers load...impossible
Lets say in these areas you mostly have families of 3 to on up in people. I'm sure these are the ones getting top dollar in stamps. So lets say you have a small 100 unit building and the average is $450 a month. So twice a month each unit is getting a box of food valued at $180. We are talking the staples...can good, rice, milk, eggs, can meat, flour, meal (5 pound each) juice many other items. You don't get that in 1 box or 2 boxes. If you can get it in 2 boxes we are talking boxes with some weight.
There is no way USPS takes that door to door...if they do they need to create a whole new unit with 1000s of trucks which means 1000s of truck drivers and then 1000s of loaders. We are talking about trucks that are refrigerated.
This is just two of Chicago's housing projects and I bet there's 10 more just as large. One is large apt building the other town houses. Now tell me how those thousands of box gets to all the units in these apts? How many trucks and people would it take to just service one of those tall buildings? Then you leave those boxes of food by the front door if no one is home? You talking a all day job for 50 people just for one building and that's if they got free control over the elevators.
Look this is just a guess on my part but you are not getting the same discount as Amazon. We are talking about more planes needed, more trucks, more workers, and not small numbers...we are talking a lot of weight in good size packing crate type boxes. To me it looks like billions of dollars being spend up front just on people, trucks, planes, forklifts, back braces and 100s of other things.
I see more of a premium charge instead of huge discounts on bulk shipping. One other thing we are talking some perishable items.
I personally don't see this happening, not with door delivery. We are talking 12 billion a year in savings...that's the government est. that's only a 18% savings. Once you contract this out I see a huge loss. Not savings. But saving or loss I don't see a way over the door delivery.
But it should add 1000s of new jobs but then again if stores are no longer getting those dollars spent locally you are taking billions out of those stores....lost of jobs.