Is this an American thing? We did absolutely not have to memorize any of that thing. We had to understand the structure, why the rows and columns etc. But memorizing it serves no purpose.
With every class including tests and exams we were allowed to use a reference book. This book was pretty thick and contained a whole lot of info including the periodic table and all the info about elements you could ever need.
I think my education (keep in mind this was 25 years ago) was focused more on the why and less on the what. If you understand why something is the way it is, the reason behind it and how to use it, you know a lot more than just being a flesh book that can list a bunch of facts.