Note that you said "car" and that's not a given. Nor is the time to go shopping and cook if you need to work multiple jobs or take care of kids or etc. It is not impossible, but there are a number of barriers that shouldn't be there.
(Edit: perhaps misunderstood what you were referring to, but if a food desert is say 10 miles without access to fresh groceries, not having a car makes that much more difficult. Even with a car, that means a larger time commitment. So I see that as part of the reasoning of what a food desert is and why that is a barrier to access to healthy food.)