I attempted to memorize the times tables. Eventually, I noticed the pattern. From then on, I used the pattern rather than memorization. For example, I compute 9*12 as 90+18.

I assume you're hinting at this, but yeah, that's the idea behind getting children to memorize and do rote math early on. There's really no better way to get people to really deep down learn strategies for dealing with numbers than repeatedly practicing and memorising stuff until they accumulate a huge bag of mental "shortcuts" and patterns and strategies they use

I don't think it's nitpicking. I think it goes to the heart of the issue: people saying "stuff I didn't use when I was a kid is BAD." The term "technology" is just being used as a veil to hide the lack of reasoning.