the analogy at the end doesn't really make sense. the goal of wriiting cursive was to speed up the ability to record information via text. typing and the ubiquity of computers has basically made cursive vestigial. memorization of facts is important to fully grasp complex problems. you don't need to sit down and memorize by staring at a sheet of paper, but eventually if you look something up enough times, you should be able to memorize it, so that you can mentally go "oh it's that" and move on, which allows you to juggle multiple of these types of things at a time.
how are you going to quickly analyze whether a fact is true without enough knowledge to verify core concepts? a better example in your rationale would be "its like saying you need to learn chemistry and metallurgy before you can become a mechanic", which is obviously absurd. but would you trust a mechanic to fix your car after a crash, or properly diagnose if it was totaled, if he had to ask you where the manual is for your car first?