It is totally possible to teach group theory at the high-school level. Instead, literally multiple years are spent teaching the quadratic equation over and over

It is totally possible to teach group theory at the high-school level. Instead, literally multiple years are spent teaching the quadratic equation over and over, and a year on "pre-calculus" which is just more quadratic equation plus memorizing some points on the unit circle. Group theory in high school would be sooo much better than the status quo. It would, however, require high school math teachers to actually learn some math.