In Learning to Bow Bruce Feiler repeats the common argument that science and maths suits rote learning more than language, but actually discovering things for yourself and avoiding a lecture style are at least as important in maths and science as they are in language teaching. If maths and science programmes on NHK Education are anything to go by, there is no lack of knowledge in Japan of how make students work together to work things out for themselves in exactly the way we TEFL teachers are taught to make our English-language students do. This means that simply teaching English in the way maths and science is taught would be an improvement!
Where Bruce Feiler does have a point is in saying that English teaching has copied Japanese language (kokugo) lessons such as the methods for learning kanji, and these are indeed less suitable for a foreign language than copying almost any other subject in Japanese schools. The other negative impact of kokugo on English is that actual lessons are as much a lesson in nationalism as they are in language, and the same is often true of English.
Another factor is that the positive things I have said about maths and science education in Japan are mainly true for primary schools, and English has until recently started in Junior High School when the rote learning is properly in control.