It's like with math. You could theoretically only memorize the axioms and rederive everything else on the fly.

But in practice, you don't have enough working memory or processing power to do that, so you'd be stuck with the math a few derivation steps above the axioms only.

To actually use math for problem solving, you need to memorize everything up to the bleeding edge, and to train yourself to operate on intermediate-level abstractions intuitively.