I think one problem is that mathematicians would have high school students focus on solving puzzles and slowly introducing technical content and proof-technique

I think one problem is that mathematicians would have high school students focus on solving puzzles and slowly introducing technical content and proof-technique, while the rest of the world cries out that they need real-world applications and preparation for calculus. The truth is that the puzzles and proof techniques are what develop mathematical thinking skills. Every mathematician knows this, but no administrators are publicly willing to believe it.