I'm not sure this is specific to any particular school of mathematical education. There is bound to come a point at which you cannot understand everything and have to start winging it. If you can cope with that, that's good, you are prepared psychologically for research mathematics. And just having learned the patterns will hold you in good stead. But if (as I did) you find the whole thing an insult to your pride then you are only preparing yourself for failure.
India (and a few other places) face this issue to a larger extent, I feel. When the judgement of your education comes via one single competitive exam, you tend to maximize that reward. In the Indian education system (and to similar extent afaik in china, south Korea and Japan), having nationwide tests that are the only factor for university admissions in math and science forces everyone competing to solve for performance in the exam. And it is far easier to do this by learning how to solve problems than by learning the material then using that knowledge to solve problems.
