Most likely, food deserts exist because we are transitioning away from an economy based on the idea of a nuclear family with a male breadwinner, female homemaker and 2.5 kids and all our benefits (medical, retirement), food culture etc. has all these baked in assumptions that mom is doing the grocery shopping and cooking for a family of four or more and that's no longer reality.
People don't have time to cook.
We haven't done enough to update our work arrangements to allow for someone to both work and eat well without mom having dinner waiting for dad when he gets home from work.
We haven't updated our food culture to allow for enough fresh, healthy options that don't take a lot of time.
I feel like advertising does so much to move the needle the wrong way, as well as services like Uber Eats. No one is out there advertising how great heads of broccoli are...its not a sexy product. But colorful Fruit Loops with 3000g of sugar per bowl that are addicting as anything I've ever come across...now there is a catch. I've also seen a shift of eating apart for families as well, I would be curious to know how many families actually sit down at a table for a nightly meal nowadays.
Most people don't actually understand the problem space. You don't even seem to understand the problem space, given your closing line:
I would be curious to know how many families actually sit down at a table for a nightly meal nowadays
The entire point I am making is that we are moving away from a life that revolves around the nuclear family. Many households in the US today have one to three members.
If you live alone or as part of a childless couple or are a single parent, etc. then this cooking from scratch "the way my mother did" just doesn't actually logistically work. And I see the evidence of this over and over and over in online forums, from comments to questions about how to cope with various aspects of the issue.
People are not happy with the way they eat and they don't know how to fix it. And the solutions we come up with are often not really very good solutions.
People don't have time to cook.
We haven't done enough to update our work arrangements to allow for someone to both work and eat well without mom having dinner waiting for dad when he gets home from work.
We haven't updated our food culture to allow for enough fresh, healthy options that don't take a lot of time.
Etc