I think it is also worth noting that virtually no highschool student is actually aware of why the formulae for third-degree equations work. Even second degree are learned mainly as formulae leading to two roots for real numbers. It would help if students actually relied less on memorizing some formulae, cause no one is going to examine something new by just parroting those.
Then again, what do you expect when almost all of the math "problems" to be solved in exams merely ask you to turn the equation into a difference or addition of squares? You don't need insight on how lego are created, if all you want to do is model the same hut 1000 times.