My education only went as far as AP Chemistry in high school but we did no such memorization of periodic table. The table is organized in a way that's extremely informative with regards to ionic charge and element classification. It pretty much is exactly what you say re: learning what the periodic table means. Any high level chemistry class that's focused on such trivial memorization is doing a huge disservice to its students.

The memorization bits come with remembering nomenclature and equilibriums, which you just kinda have to memorize or you're not really learning any chemistry at all. They're the building blocks of all higher level chemistry that come after, organic or inorganic.