How is learning all the special cases of the triangle manipulation (O-plus when its bottom right and the top is missing but multiply in the bottom left, multipl

How is learning all the special cases of the triangle manipulation (O-plus when its bottom right and the top is missing but multiply in the bottom left, multiply when the top is given and bottom is missing etc) better than just learning the different notations? Not to mention the existing mathematics you miss out on by using this. That being said I think it's a fantastic tool to quickly explain the relationship between the notations (the first half of the video).