> If you believe that the only role of schools is to teach useful skills, then you are correct.

I believe the role of schools, especially before and during high school (it's another matter for college/uni) is rather to teach basic skills (read, write, count, know a bit how the world works and how to think) and to teach how to learn, and also what exists that could interest you.

Teaching only useful skills is very simplistic and even seems to me like a bad idea, and I think you demonstrate why in the rest of your post.