Then I read in other comments about US math curriculum and I was shocked to learn that not only they were NOT doing this, but they didn't have a better alternative. This is mind boggling. It seems almost idiotic.

My schooling was done in India. Our curriculum was quite well planned, but what is laid out here is the methodology of teaching in addition to the curriculum and textbooks. And that depended on teacher to teacher and school to school. But nonetheless, the textbooks were very well written so everyone got exposure to pretty much the same level of teaching styles, more or less.

When I came to US in college, I was surprised to learn that people didn't know basic techniques and tricks for algebraic manipulations. Of course, we were taught the basics and whys behind every trick but emphasis was also given to internalizing these tricks for quick computation by hand. This, in my opinion, is important because these tricks also become your mental models when thinking about math. And quick tricks would lead to quick thinking, roughly speaking.