Right. I learned what binary trees were in college and didn't directly use them much afterward. Since interviews sometimes ask about trees, I started my practice of solving tree problems by practicing how to invert a binary tree. I practiced it so much that I can invert a binary tree from memory now, so that I won't get bounced from an interview like the inventor of Homebrew was from a Google interview.
Most of the concepts I learned, although I don't remember learning Kadane's algorithm for solving the maximum subarray problem in school, so I've learned some things like that. I can also implement a solution for an associated Leetcode problem in one line of code, so I wound up memorizing that too.
OP says "If you master the methods and ideas, you should be able to derive the answers on the spot", but I hear from a lot of people that does not happen, even (implicitly) in this thread. Any how, even if I use OPs method, if I do the same problem over and over and over again I'm going to wind up memorizing it any how.