You seem to imply that actual mathematical content is rather less important. Then why stick with algebra and calculus?

Frankly, I agree with Hacker: quadratic equations are boring. Teaching number theory will do better job of teaching pattern recognition and deduction. More Fermat's little theorem, more Chinese remainder theorem, less quadratic equations. I found undergraduate number theory to be far easier and more fun than calculus, and you need no calculus to start on number theory.