Do you have anything to support that? It seems incredibly unlikely. Food deserts aren't devoid of retail altogether. They're not even devoid of food retail. They just don't have supermarkets.

Sure:
corporate.walmart.com - Walmart announces closure of four chicago stores

The simplest explanation is that collectively our Chicago stores have not been profitable since we opened the first one nearly 17 years ago – these stores lose tens of millions of dollars a year, and their annual losses nearly doubled in just the last five years. The remaining four Chicago stores continue to face the same business difficulties, but we think this decision gives us the best chance to help keep them open and serving the community.

Many stores lose money in low income areas - crime being one factor - and other stores in the chain have to pick up the slack. As for these 4:
dailymail.co.uk - The stores closed doors rampant theft

...it's not just Wal-Mart:
Major retailers in the US have been forced to shut down stores due to millions of dollars in losses as rampant theft plagues big box stores across the country.

This week, Walmart announced it will shut down four of its stores in Chicago just weeks after America's biggest employer shuttered its only stores in Portland.

It comes as shoplifting reaches alarming levels and other large retailers, including Target, Macy's and Best Buy, are now making good on threats to shutter outlets if petty crime was not lowered.

In 2021 retailers lost a combined $94.5billion to shrink, a term used to describe theft and other types of inventory loss. And organized retail crime incidents soared by 26.5 per cent in the same year, according to the 2022 National Retail Security Survey.

Here are some estimates for Target:
apnews.com - Target first quarter earnings inflation shoplifting
Target said theft is cutting into its bottom line and it expects related losses could be $500 million more than last year, when losses from theft were estimated to be anywhere from $700 million to $800 million. So that means losses could top $1.2 billion this year. The company said it’s seeing an increasing number of violent incidents at stores as well, but does not want to close stores and is expanding security and locking up some items.

What does $1.2Bn in losses mean for them? Let's look at their income statement:

Yahoo Finance: Target Corporation (TGT) Income Statement

If we take ~$4Bn to be their average net income, then a loss of $500M/year represents 12.5% of their overall profit. That's a lot of money to have walk out the door. Literally.

And the sorts of products that supermarkets sell are particularly ill-suited to resale after shoplifting (they tend to be inexpensive, bulky, sometimes perishable, subject to damage if compressed or pushed into something, and fungible commodities).

Al, al, al. My friend.

Oh, you have so much to learn about street culture and open air markets!

Bottles of Tide are item #1 for most "Street entrepreneurs". It's so bad that at most Seattle-area stores they have to lock up their detergent aisles.

theatlantic.com - Why are criminals stealing tide detergent and using it for money

And this is from 2012! It's gotten much worse since then:
Earlier this week, The Daily's M.L. Nestel wrote that Tide liquid laundry soap appears to have become a favorite target of shoplifters around the nation, who are jacking the product from store shelves in bulk, then selling it on the black market. Thieves simply load up shopping carts full of the bright orange bottles, then bolt out the door. One con in Minnesota appears to have liberated $25,000 worth of the stuff in 15 months before he was eventually arrested. Meanwhile, police in Prince George's County, Maryland have taken to calling Tide "liquid gold." According to the Associated Press, officers there say that drug dealers have started urging their clientele to pay with Tide bottles in lieu of cash.

By why Tide, of all things?
Criminals tend to pilfer products that are small and expensive -- razor blades, infant formula, gift cards, teeth whitening products, cosmetics, and over-the-counter medications, for instance. While it's a little bulkier than most of the items on that list, a bottle of Tide would seem to make a good target because it's a leading brand, everybody needs it, and it's pricey; one bottle can cost up to $20 retail, and it allegedly sells on the street for between $5 and $10.

Plus it's chemically stable to store and never goes bad. What's not to love?