Potatoes and sweet potatoes are very cheap and you can practically live on them, in perfect health. Generations of Irishmen, Kitavans, and Peruvians have. This claim that you can't eat healthy on the cheap is silly. Eating just potatoes & butter & a few eggs a day and you could probably go years before having problems. The prep time argument is also silly. A sack of potatoes will keep for a month and you can boil or nuke a potato in minutes.
The "convenience" foods are about the taste and pleasure. It's not cost or convenience. Junk food and fast food are very tasty and offer variety, unlike plain potato, or some other reasonably nutritious gruel.