In my high school experience, this was avoided if you had the desire and aptitude to just take Honors Physics instead.
To work around the fact that many of us were still in precalc, our teacher just taught us the power rule, the relationship between slopes of tangent lines, etc., without diving into the "why" of why those things worked.
That said, yeah maybe for the most basic of university of physics the whole "derive it on the fly" strategy works, I guess? But when you get to more advanced courses like mechanics of materials, you'll do yourself the favor and take to memorizing at least a few of the commonly used equations.
