You need to afford a computer of some kind, afford the premium for food delivery, and have a debit card in order to have fresh food show up in your food desert. Most people for whom living in a food desert is a problem are impoverished, and therefore don't have a car, don't have a phone/tablet/computer, and often don't have a debit card, and certainly won't pay the delivery premium. So this is not in any way going to help those living in fresh food deserts.

Poor people have smartphones at a rate far higher than you would expect, partly because it's practically necessary these days, but also because you can get one on a plan from your carrier.

Delivery costs are a real issue, but I have a hope that we will get self-driving trucks in the near future and delivery prices will fall.

Amazon has a gift card system (Amazon Cash I think?) and as a full blown grocery store could accept EBT.

Doubtful.

The kinds of foods needed in those areas are fresh, cheap, high spoliage items aka unprofitable to touch unless in bulk.