It appears that you have completely failed to realize that your example from British private schools regarding memorization is used to weed out the "riff raff" as it were. Don't want to hire "brown people", women, or other non-white privately-educated individuals? Institute a British-styled rote memorization test and make claims that it is fair because, "anyone can learn the requisite knowledge."
Whiteboard interviews are actually quite similar in both their implementation and impact!
It sounds so innocuous... "Cultural fit." But wow does its meaning become sinister when used in the context of (illegal) discrimination.
And since this is about historical reality, we know that the British public school system of rote memorization of Greek and Latin texts, along with translation into and out of Greek, did produce capable people who built up an empire and maintained it for many generations.
Rote memorization of Greek and Latin texts probably had very little to do with the expansion and maintenance of the British empire.
TL;DR: Seriously?
No, but the sorts of schools that required rote memorization of Greek and Latin texts tended to be 'good' schools that also taught other things that where considered useful (including things like how to behave in a 'proper' British manner) . Testing for Latin knowledge was a proxy for testing for a good general education from a good school.
Writing pseudocode you've memorized from a book is fundamentally meaningless. You have to realize it isn't really a programming test: it's a filter for whether you're willing to do what's required to fit in.
The principle is the same as in classic British private schools where boys were required to memorize long passages of ancient Greek and Latin texts. In fact, tech companies would probably get the same hiring results by replacing Cracking the Code Interview with Ovid's Metamorphoses, and asking about Phaethon's fall instead of binary trees -- the substance doesn't really matter. (The non-whiteboard parts of the process would do the same job as they currently do of ensuring some degree of practical software competence.)