Isn't the structure of the school curriculum also at fault here? If concepts like the quadratic formula being presented without context on why you will need to memorize them, and you're able to succeed without doing it, it's clear why you might choose not to memorize it. That wouldn't be the case if they presented you with challenging, applied problems where having the quadratic formula memorized really is actually necessary.

The curriculum seems to be structured under the assumption that the students will memorize the facts for the sake of memorizing (as most students do) in order to get good grades, and only later apply them on more advanced classes. If you're able to derive the results fast enough, and as such you see no point in memorizing them, then that assumption is broken, and the curriculum won't work the way it is expected to. Those students would need to take initiative themselves to adapt their learning style to the way books and classes are structured, as it's not obvious for them that such memorization is necessary.