Neither students nor practitioners derive formulae from first principles each and every time,

1. If they have it memorized, it's from years of usage, they didn't need to practice moroizing the things theyd use every day. Because it would happen anyways.

2. Math class isn't applied Math, it's just Math. Giving credit for memorizing someone else's equation is a way to push people thru who can't do the math.

And even in a hypothetical world where someone needs to apply an existing mathematical formula that they don't use constantly, they're not gonna just risk it to save 2 seconds checking.

I understand why you have the opinion you have, but that doesn't mean our education system was blinded in the pursuit of metrics generations ago, hell, it's ancedotal evidence it did...