>> Same reason we used to read Euclid in class and make students demonstrate countless proofs.

Key phrase: "Read Euclid". American schools do not read about math. They are taught to do math. They do not read anything written by the people who created it. They are not given context. They are given set problems and taught how to solve them using prescribed methods. More often than not, this results in lackluster understanding.

I did an AP course at school where we had to write a paper on a subject. Not a problem set. Not a proof. An actual paper about a mathematical concept. I did mine on the mathematics behind various methods for counting cards.