Bring back neighborhood grocery stores you can walk to.

This is actually probably more a federal antitrust/competition law thing than a local zoning thing. Otherwise it wouldn't have happened nationwide. I found this article to be pretty persuasive:

Food deserts are not an inevitable consequence of poverty or low population density, and they didn’t materialize around the country for no reason. Something happened. That something was a specific federal policy change in the 1980s. It was supposed to reward the biggest retail chains for their efficiency. Instead, it devastated poor and rural communities by pushing out grocery stores and inflating the cost of food. Food deserts will not go away until that mistake is reversed.

. . .

Congress responded in 1936 by passing the Robinson-Patman Act. The law essentially bans price discrimination, making it illegal for suppliers to offer preferential deals and for retailers to demand them. It does, however, allow businesses to pass along legitimate savings. If it truly costs less to sell a product by the truckload rather than by the case, for example, then suppliers can adjust their prices accordingly—just so long as every retailer who buys by the truckload gets the same discount.

. . .

During the decades when Robinson-Patman was enforced—part of the broader mid-century regime of vigorous antitrust—the grocery sector was highly competitive, with a wide range of stores vying for shoppers and a roughly equal balance of chains and independents. In 1954, the eight largest supermarket chains captured 25 percent of grocery sales. That statistic was virtually identical in 1982, although the specific companies on top had changed. As they had for decades, Americans in the early 1980s did more than half their grocery shopping at independent stores, including both single-location businesses and small, locally owned chains. Local grocers thrived alongside large, publicly traded companies such as Kroger and Safeway.

With discriminatory pricing outlawed, competition shifted onto other, healthier fronts. National chains scrambled to keep up with independents’ innovations, which included the first modern self-service supermarkets, and later, automatic doors, shopping carts, and loyalty programs. Meanwhile, independents worked to match the chains’ efficiency by forming wholesale cooperatives, which allowed them to buy goods in bulk and operate distribution systems on par with those of Kroger and A&P. A 1965 federal study that tracked grocery prices across multiple cities for a year found that large independent grocers were less than 1 percent more expensive than the big chains. The Robinson-Patman Act, in short, appears to have worked as intended throughout the mid-20th century.

Then it was abandoned. In the 1980s, convinced that tough antitrust enforcement was holding back American business, the Reagan administration set about dismantling it. The Robinson-Patman Act remained on the books, but the new regime saw it as an economically illiterate handout to inefficient small businesses. And so the government simply stopped enforcing it.

That move tipped the retail market in favor of the largest chains, who could once again wield their leverage over suppliers, just as A&P had done in the 1930s. Walmart was the first to fully grasp the implications of the new legal terrain. . . . Kroger, Safeway, and other supermarket chains followed suit. . . . Then, in the 1990s, they embarked on a merger spree. In just two years, Safeway acquired Vons and Dominick’s, while Fred Meyer absorbed Ralphs, Smith’s, and Quality Food Centers, before being swallowed by Kroger. The suspension of the Robinson-Patman Act had created an imperative to scale up.

A massive die-off of independent retailers followed. Squeezed by the big chains, suppliers were forced to offset their losses by raising prices for smaller retailers, creating a “waterbed effect” that amplified the disparity. Price discrimination spread beyond groceries, hobbling bookstores, pharmacies, and many other local businesses. From 1982 to 2017, the market share of independent retailers shrank from 53 percent to 22 percent.

The whole thing is worth reading.