The point is, for many of us, the best way to “memorize” things is to explicitly avoid trying to memorize them, and focus instead on understanding context and connections between things – after you’ve had to call up the same idea 5 or 10 times because it was related to something else you were learning about, recall just comes along.

Examples I’ve often seen used by proponents of rote learning include multiplication tables and spelling lists. I’m better at mental arithmetic than almost everyone I know, and I almost never misspell words, not because I spent any effort memorizing lists of them (indeed, I completely refused to do this as a 9-year-old, because it bored the crap out of me), but because I’ve spent more time in exploratory play with the relationships between numbers than they have, and have spent lots of time reading, doing close textual analyses for my own edification, trying to write tight fluid prose, and playing with various kinds of poetry, etc.

I’m convinced that rote memorization is promoted as a pedagogical tool because it is cheap and easy and requires little effort from teachers and schools, more than because it’s particularly effective. Then again, everyone learns differently, and I know some people who are incredible at chewing through lists of facts once quickly and dredging them back up effortlessly months later. YMMV.

This sort of thing seems to me to be just you stumbling on the spaced repetition effect by accident: you look up the same thing several times, at varying intervals as you learn it more.

I personally think multiplication is actually a great thing for spaced repetition if you can get the software to pick random numbers each time. I also find that things that I don't review regularly just fall out of my head, spaced repetition software is good for just stopping that relatively easily.

Speaking only for myself, learning things rote, via software-driven spaced repetition or otherwise, is deadly dull. On the other hand, finding new patterns, reading relevant books and deconstructing their arguments, holding discussions with other people passionate about a subject, trying to construct new ideas and relate them to past knowledge, etc. is exciting and invigorating. Living life as a human rather than a robot may be less than perfectly efficient relative to some platonic ideal, but really, so what? Similarly, I’d much rather go on a hike than run on a treadmill, I’d much rather cook and eat a delicious meal than compute the perfect mixture of nutrients and blend them into a shake–slurry, and I’d rather make one deep friend than fill a rolodex with business cards. My personal impression from having dabbled with spaced repetition software after a friend bugged me about it for months was that I personally learn better when learning things doesn’t feel like a visit to the dentist. Call it a character flaw. Again, YMMV.

My point about the multiplication tables and spelling lists though was that explicitly learning e.g. multiplication tables is pretty much unnecessary, because multiplying small numbers comes up again and again in doing more exciting and challenging problems, and by the 20th time you’ve had to multiply 6*8 through some explicit manual method, you’ll just start to remember that oh yeah, that’s 48 again.

While I agree that rote learning is very dull, it can be fundamental in situations where you know next to nothing of the subject at hand.

Consider for example two native English speakers, one learning German and the other learning Chinese. German grammar is way more complex than Chinese's, but because of the etymological closeness between German and English, the German student will quickly get to the point where they can easily pick up new words from the context (obviating the need for vocabulary lists), while the Chinese student will pretty much never reach that. In this type of situation an SRS is invaluable.

Regarding multiplication tables, you shouldn't forget that knowing them by heart is sometimes necessary for understanding the exciting problems. This comes up all the time in mathematics: to understand the important problems in a field, you sometimes have to get to know well a lot of seemingly boring concepts.

Knowing multiplication tables by heart is never necessary for understanding exciting problems; the exciting problems are not dependent on your arbitrary culturally-contingent choice of numeric base! I had discovered the commutative and associative properties of multiplication long before memorizing multiplication tables in fourth grade, and historically speaking, they were known long before the adoption of place-value numerical systems.

It might be essential, but it's also overrated as a primary measure of mastery. The more difficult the subject matter, the less useful rote memorization is in the end; there were plenty of people with near-photographic memories that I saw failing upper level math courses at university. And I knew plenty of people that excelled at that level but had to look up specific formulas all the time (as best as I could figure, they tended to remember quite well what transformations the formulas allowed, just not the exact form that they allowed them in).

That said, it's certainly not going to hurt anyone to increase their rote memorization abilities, in fact it's probably extremely useful in general, no matter what field you're in.