The last thing you said is what I came in here to write. Everything in the NYTimes article is correct (about how easy it is to cook those 3 basic meals etc), but it misses one thing: there is no way that someone goes from eating burgers and prepackaged foods to salads and lentils instantly, and it's not because it's difficult or time consuming to cook (it's not really for most things).
Restaurant food has a major convenience factor, but the NYTimes article completely disregards that it also just plain tastes better than a salad to most people.
As someone who hates healthy food, lives in NYC where I can literally order delivery off the internet, and is trying to cook a lot more, you can't force two things on people at once: healthy eating AND cooking. I'm beginning to really like cooking, but only because I'm making things that aren't super healthy. My mother is a librarian and highly encourages her kids to read comics because to her they are a) totally valid reading material and b) are sometimes a gateway drug to much more reading. It's the same with cooking: teach someone to cook a butter burger and fry up some potatoes first (they'll still probably be knocking a few hundred calories off a restaurant version of the same meal anyway) and get them hooked on it. Maybe they'll transition to healthier stuff, worst case you at least have them eating SLIGHTLY healthier, and far closer to the source.
TLDR: Make a man a salad and he will order delivery for a night, teach a man to make salad and he will order deliver for a lifetime.