As I briefly mentioned in a lower comment, why can't high school be for "breadth", while university is for "depth"? More people would benefit from this, since most people go to HS, and it would also be cheaper on both individuals and society.
History, logic, basic mathematics, languages (both native and foreign), geography, and many more are covered by high schools curricula all over the world.
Edit: I think this idea that college needs to be "broad" also creates further craziness in how some of the "deep" education is structured: you go to law or medical school after 4 years of college. In other countries, law and medicine are university specialties (in my country, for example, medical school takes 6 years of university education; in the US, first you get 4 years of college, then 4 more years of medical school).