Schools should probably also have cooking classes. Eating is something everyone does three or more times a day. Why not learn how to do it right. I’m sure something like that would have a huge ROI for state and local governments.
Taxing sugar is not an incentive to sell more nutritious food, unless we're taking those taxes and subsidizing produce with them. Those sweet, highly-processed foods are also a way better purchase for grocery stores, which don't have to worry about the food going bad before it's purchased.
I do think banning these types of stores is likely to cause more harm than good, though. To take it to extremes, there's simply never going to be a farmer's market where my closest Dollar General is.
Also, healthy food is cheap, but people buy junk because it is superficially more fun. Compare what you get from $10 of Lucky Charms vs $10 of veggies, beans and cheese, and, if you must, simple bread and low quality cuts of meat.
$10 in dried beans is lunch for a month, but it's damn inconvenient, and yes, difficult to make taste good.
These are both extremes but yes, I am very confident that healthy food is more expensive than less healthy food. Yes, a cucumber is "cheap". But 8 cucumbers (.50/each) isn't going to get you nearly as far as a 6pack of GV mac and cheese ($3.98). Not even the same ballpark. 5 servings of GV thin-sliced honey ham costs $2.50, a loaf of the cheapest white bread is $1.50, 8 servings of GV block cheese goes for roughly $2.22, so now I have let's say 10 shitty sandwiches for roughly $8, when I could have had easily 12 meals of mac & cheese for half that and with less prep time.
Where cheap and healthy come closer together, I see the staples of my (well, my friends', but that's another story) childhoods; lots of potatoes, scrambled eggs, beans.