Ah, a belated sequel to “French Women Don’t Get Fat” 
The article, of course, as often tends to happen with many of these, oversimplifies and under-thinks, especially in its conclusions. Sort of disappointing from the author of a book called “Food Intelligence”.
But aside from that, a few disparate thoughts.
It’s good to see mention of frozen and canned vegetables in regular use, because any discourse on healthy eating in the US inevitably gets linked to fresh fruit and vegetables, food deserts, and so on, which is valid and important, but a different discussion. Access to frozen and canned is still access to healthful options, but after that comes choice of whether to include those things. There are plenty of conveniences available at every price point in the US to assemble a more healthful meal than fast food – however knowledge, education, or instruction about that isn’t as popular.
“By buying and preparing farm-fresh food, Americans could reclaim their health and repair the food system.”
This projection is one of the key hurdles to actually solving anything. Making people think the only healthy choice is shopping at farmer’s markets or participating in CSAs sets up a hurdle few can overcome. Instead, why not promote frozen and canned vegetables as healthy choices too, especially when frozen have repeatedly been proved to be such, and are easily and cheaply available in most areas?
“The burden of food procurement and cooking is still shouldered overwhelmingly by women, most of whom now also work outside the home. Asking people to cook more is usually asking women to cook more. Even in households that want to make every meal from scratch…”
Again, this is mixing up several separate points – invisible load / labor, cooking from scratch vs assembly for healthy meals, a living wage these days vs in prior generations providing references for the “traditional” concepts of food and family (that make it not always a choice, rather a necessity, for more external working hours for all genders), and more.
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Nutrition education (or the lack of it), changes in the structure of society, inflation in cost of living vs wages, and the influence and control of Big Food, Big Agro, Big Pharma, etc. aren’t political, purely factual.
Painting them as political is what prevents positive change.