I'm not saying that rote memorization is the end-all-be-all or that it trumps critical thinking. It doesn't. But neither is it unimportant.
Try talking history and not know your dates. You needn't remember exact dates but knowing that Augustine lived around 360-430 and was not a contemporary of Aquinas (1225-1275) who was not a contemporary of Hobbes (born in 1588 - the year of the Spanish Armada) is important when in the field.
Knowing that Babe Ruth and Derek Jeter were not contemporaries is also import. Joe Louis did not fight Muhammad Ali who was not a contemporary of Mike Tyson. All these items (when people lived, when they were active in their respective sport) are facts - not critical thinking. Judging the relative merits of Joe Louis and Mike Tyson takes critical thinking.
Doctors memorize bones and muscles. It's important but rote memorization of these facts will not make them good doctors (and is probably not enough to graduate).
Learning how to memorize helps one derive mnemonics - like the phone number 10-4-3-4-1-1-1. (Yes it's not a real telephone number) and then use that to help remember key facts. A US citizen should be conversant with the constitution even if they are not a constitutional lawyer. The Constitution has 7 parts (articles) each with different sections. The first article, which deals with the Legislative Branch, has 10 sections; the second article, which is concerned with the Executive Branch has 4 sections. The mnemonic 10-4-3-4-1-1-1 helps me remember, to mentally categorize key points about the US Constitution.
Will memorizing the constitution make me into a jurist ? No. But the effort of learning involves memorization.
Memorization is to cerebral activities what wind sprints and sit-ups are to athletes. It helps one become better and while sit-ups won't turn me into a world-class boxer or football it is a necessary part of becoming a world-class athlete.