During sixth form college (ages 16-18, in the UK) one of the philosophy lecturers started a course with the same sort of goals. It covered critical thinking, written communication, logic, a bit of psychology etc.
The 12 or so hours I spent in those lectures were among the most valuable hours I invested in anything, ever.
There is still, to this day, a large number of people who think education needs to be repetitive rote drill in order to be... real, or legitimate, or even 'useful' by some warped definition of that concept.
It's tied into the notion of hazing, or "If I had to waste my years in school tied to a desk memorizing stuff I don't use, so should you! Builds character!"
And, finally, the idea that if the next generation does it, too, maybe your time doing it wasn't simply wasted.
-numeracy: how much is 1 million/1 billion/1 trillion, etc.
-common cognitive biases.
-logical fallacies.
-basic science.
-basic coding.
-De Bono's 6 thinking hats.
-how the brain works.
-meditation (ie not thinking).
-how to learn stuff faster and better.
-how to remember stuff: memory palace and the like.
-etc
I could think up a HUGE list of stuff in this genre that would be very helpful.