Via Jacob A. Geller, the evidence is now in and it seems to suggest no, food deserts are not a real problem:
Here is more, and here is the study itself. If you look at the statistical tables, they’re pretty striking. Even where there is statistical significance — which is the exception to the rule — the size of the effect is so tiny, it’s like practically nothing. For example, on the margin, adding one full-service supermarket within a one-mile radius of your house is associated with an average BMI decrease in your neighborhood of .115. That is a difference of just one pound. (See back-of-the-envelope calculations here.)
So there is really no relationship, according to this one recent study of nearly 100,000 Californians, between the distance between your body and a full-service supermarket (or any other kind of food store), and whether or not you are obese. Distance, which is a proxy for access (the idea of a food desert is that the nearest supermarket, which has fresh produce, is distant), is for all practical purposes a non-factor.
Here is a good example:
For example, when you last ordered food at McDonald’s, did you even notice those ten salads on the menu? Did you order them? No, and me neither. And did you ask for a cup of water, which is free, instead of a soda? No again. (That’s my experience anyway, and that of millions of other Americans.)
And an excellent parallel:
And what’s interesting from a political standpoint, is that this analysis similarly applies to drugs — tackling the supply side does little for heroin addicts, for example, increases the price of heroin, which induces supply to come back into line with the addicts’ inelastic demand curve — and yet most liberals would probably agree with me that drug addiction ought to be tackled on the demand side (spending money to convince young people not to shoot up heroin for example, instead of spending money on patrolling the border), but the same liberals who agree with this analysis of the drug war will often turn around and favor unproven supply-side solutions to obesity like subsidizing supermarkets in low-income neighborhoods, despite the absence of evidence to support those ideas. Note that libertarians are more consistent on those issues — they oppose supply-side interventions in most, if not all, illicit drug markets, and also oppose supply-side interventions into food markets.