You know what I think is a myth? That it's cheaper to live off unhealthy food than it is healthy food. Buying, for example, loose potatoes is cheaper than buying chips (fries, if you're American), and you don't have to cover them in grease and fat when you cook them. I think it's unquestionably true that going to McDonald's is more expensive than cooking for yourself.
Of course there will always be instances of certain healthy foods that are cheaper than certain unhealthy foods and vice versa. It's silly to make broad generalizations either way.
It seems that research which looks at how expensive various foods are in comparison to how healthy they are tend to assess price per calorie (like
this study, which found that healthy food is 3x as expensive as non-healthy food). But part of what classifies a foodstuff as more healthy is that it has a lower energy density than the less healthy foodstuff. This is especially true if what you're looking at is weight loss.
I love how that study combines "meat, fish, eggs, beans and other sources of protein" into one category and shows them at around 4 pounds per 1000 kcal. I've bought beans for the dollar equivalent of about 0.20 pounds per 1000 kcal (20 times less!). Meat, fish and eggs are way more expensive than beans. It's a very misleading display. It makes about as much sense as averaging a six pack of Blatts beer and some over-priced elitist wine and concluding that "alcohol costs about 50 dollars per gram".
"Foods high in fat and/or sugar" is such a broad/unclear category. Is fruit high in sugar? Is meat high in fat? How the heck high is high. They say "We classified food items in our new dataset according to five distinct food groups, defined by the Eatwell Plate—a tool for nutrition communication developed by the DH to define a healthy diet." So I assumed "the Eatwell Plate" offered some sort of objective criteria for classification. But as far as I can tell "the Eatwell Plate" is just a graphic of a pie chart that looks like a plate.
I also note that what they have displayed as the cheapest category (rice, pasta, bread, potatoes) is something that "the Eatwell Plate" recommends eating plenty of.
They are right that vegetables and fruits tend to be high in nutrition, but relatively low in calories. And that they are, thus, more expensive per kcal. I thought that was common knowledge. But other than that, the study seems like junk.
The chips have more than twice the calories for roughly the same price. This means that they will be counted as more than twice as cheap by studies such as the one linked above, yet if you're trying to reduce your calorific intake, then the potatoes would be the better option, would they not?
When they say "cheaper to live on" they're just referring to calories, as that is the most basic thing you need from food in order to sustain yourself and to feel psychologically okay (not suffering from hunger pangs) in the short term. If all one cared about was calorific intake and price then they should buy the chips over the potatoes and simply eat less of the chips per day. I could reduce my calorie intake to 1000 per day eating an all-twinky diet - a pound of feathers doesn't weigh less than a pound of lead. (Of course, that's assuming perfect self control and calorie monitoring. It's easier to over-eat on some foods than others.)
So, no, I don't believe that it's cheaper to eat unhealthily than it is to eat healthily. I think that the usual method of assessing the expense of food is unsuited for this purpose, as it necessarily means that foods which are lower in calories are deemed more expensive than those which are full of calories. It's front-loading the results into the testing method.
You need some basis for measuring "expense" and calories per dollar is one way of doing it that does make some sense, to a degree. Nutrients per dollar is another way to do it, but it wouldn't make much sense to define expense by nutrients per dollar and then comment on whether expensive foods are more or less healthy than inexpensive foods. I think going by the weight and/or volume of the food makes the least sense, but it's not a worthless consideration. When it comes down to it, though, if you're poor and hungry you're probably going to prefer calories over micronutrients or weight/volume every time.
I still think eating healthy is cheap if you know how to do it. Beans are amazing value, not just for calories, but for protein, vitamins and minerals as well. An electric pressure cooker makes them ridiculously easy to cook. And a little bit of vegetables goes a long way. That was another misleading grouping, because there is a lot of variation in fruit/vegetable price as well. Green cabbage - amazing value. Apples - not very good value.