When I lived in West Philly, I often bought my fruit and veg from a truck. It was cheaper and better that the chain grocery a block away. I think low cost options like the Arabbing in Baltimore or several food trucks going to these neighborhoods would have worked better and been more cost effective than whatever the govt did.
One of the problems with ‘food deserts’ - we had a chain grocery store, but it wasn’t very good. We also had people with various income levels, many of whom could have paid for a better selection. The problem in a lot of cities (at least on the east coast) is that people don’t have cars. This makes it difficult to do major shopping elsewhere if you can’t find what you want nearby.
Online shopping is helpful (I did it all the time in Seattle, being carless there as well), but I don’t know how many of these services will go to hardcore inner cities.
I wore out several of these when I lived in Philly:
The only time those got a break was when I was pushing a stroller, which also had a wire basket on the back, and you could hang plastic bags on the handles. Then there was the double baskets on the back of my bike...
...and also the child seat, where you could strap a grocery bag or a watermelon in place as long as the child wasn't along for the ride.