Having earned an undergraduate degree in math I've often had similar thoughts about US elementary math education's emphasis on rules and mechanical calculation and memorization rather than more abstract concepts like pattern matching.

Turns out there was a thing called "New Math" (https://en.wikipedia.org/wiki/New_Math) in the 1960s where public elementary schools tried to teach concepts from set theory and abstract algebra. Basically everyone hated it.

Perhaps there was just a curriculum failure, or perhaps teachers weren't well-equipped enough to teach the material. But we can't ignore the attempt and need to come up with an answer for why New Math failed before we can try it again.