In fact, the Soviet approach also emphasized solving problems. There are books entirely devoted to problem sets, and there are other books devoted entirely to theory. My grandfather was a Professor of Mathematics at Moscow State University before we emigrated, and as I was growing up, he would always stress that it does one no good to just know about swimming if you can't actually swim. The people who learn the most are the ones who have competency in both theory and application. To get that competency, you alternate between focused practice in one and the other, just like an athlete alternates training different muscle groups.