"Personally I think it's the "everyone should do everything" attitude that is the root of the problem. "
But if "everyone should do everything" is removed, who gets to decide who does what? What if the next Einstein or Hawking gets directed to needlework, arts and crafts instead of science and never finds out they have an aptitude for inventing the first FTL drive?
Give the youngest the basic, including social skills, the middle group some of everything and the oldest get to choose their areas of special interest. Pretty much how education works across much of the world now.