Where the poor are actually miles away from grocery stores without mass transit is in rural areas.
Or suburban areas, or poorer cities, or small towns, or any city with distributed locations of employment.
The city I live in, Albuquerque, has mile after mile of residential zoning but buses seldom run in the evening or on weekends. There's a grand total of one (1) way to cross the river by bus in the evening or on a Sunday. Population of the city and the immediate surrounding area is over 1 million, but half the city does not have sidewalks. There's no such thing as a subway or a light rail system here. But it's situation normal throughout the West and the South.
The only places in the USA that have actual non-trivial mass transit outside the downtown core are in cities or states that are either very wealthy, or have been wealthy in the past.
A person doesn't have to be miles from a grocery store to find it physically difficult to get there. Even one mile through a neighborhood with no street lights and no sidewalk is dangerous and physically challenging to an able-bodied adult carrying groceries. They are not physically navigable to someone who relies on a wheelchair or crutches, or who is burdened by small children, especially in bad weather.
But broadstroke use of the term food desert is a misnomer. It isn't the cause of obesity among the poor, not even close. Particularly the urban poor. Good food options abound for them.
And I know this because in the 1990s, I worked on the technology to migrate from paper food stamps to EBT cards. The distribution system to get food to where people are and to transport people to food has never been as good as it is today.
There are definitely other contributing factors. The type of food that is available when a person is growing up tends to be what they select when they have a choice. Presently, what's available in schools is pretty much mall food court food: extremely greasy, fatty, salty, oversweetened, and loaded with preservatives and other things that make it easy to prepare in large amounts and hold indefinitely. Anyone who grows up eating slop like that tends to prefer it as an adult. We also market to kids using the TV, and children's cereals and other food tend to be unhealthy, over-sugared rot. Poor people are exposed to more TV and more advertising, and it does have an effect.
Logistics-wise, food quality was phenomenally better in the 1950's when backyard gardening, home canning, and family farms were common and when many commodities were delivered free of charge. Ever since people started relying on commercially manufactured and distributed food, they've had to go outside their immediate surroundings to get it. They've also have to pay for layer after layer of oversight, inspection, packaging, and "safety" features that make food more expensive to deliver unless it's mass produced glop.
Homemade food or fresh food doesn't scale well enough to be commercially viable in a neighborhood distribution system. One thing that can be said about shelf-stable processed food is that it does scale and transport well.
There are also all kinds of hoops to jump through in order to sell food to the public. For one thing, it's illegal to produce it in your own kitchen: you have to have a whizbang commercial kitchen that you don't do your own cooking in, there have to be all kinds of inspections and licenses, and you can't just set up a hot dog stand on a street corner. It's illegal. If you get caught, the police can and will physically take your inventory and shut you down. Unlike a drug dealer, a person who makes their living selling food needs an onsite way to store, prepare, and distribute it.
So yes, where there is sufficient customer demand, there is a supplier. Insanely easy to buy H, probably in your own neighborhood. If the demand is for apples, kale, rice & beans, the guy on the corner will sell that, too.
And promptly get shut down by the FDA for not labeling and packaging the produce properly, or by the local city authorities for not refrigerating the product at the right temperature. If something goes wrong and a person gets sick from eating the product, expect lawsuit after lawsuit until the seller goes bankrupt or out of business. These are things I'm no drug dealer has to worry about. Unlike illegal drug dealers, food sellers who don't jump through the hoops and follow the rules get physically shut down. There's far more interest devoted to making sure people don't sell homemade burritos on the street corner than there is in making sure people don't sell sex or pot.
There are substantial barriers to entry if you want to get into the food selling or distribution business. I looked into it a couple years ago because people are very fond of my homemade jams and jellies. So I ran an analysis. It turns out that if I complied with all the packaging and preparation laws, I just can't get my production costs low enough to compete with commercial glop unless I either subsidize the purchases out of my own pocket and run at a loss, or do exactly as the commercial producers do and sacrifice quality.