One aspect of teaching everyone to code is what Seymour Papert talked about in Mindstorms: it can be used as a medium for carrying ideas. For example, I think Mindstorms had this anecdote about a child who previously had trouble grasping the idea of classifying parts of speech (nouns, verbs, etc.). Later, she was writing a program for creating random nonsensical sentences, when suddenly it clicked, and it all made sense to her.

The point of this anecdote is not that every child should write such a program to understand parts of speech. It's about something much more general, but I have no idea how to express it briefly. I'm not even sure if I fully understand it. So, unfortunately, this idea might just be too subtle to be properly executed on a national scale.