For the first point, you are right, sanrensei is not very common since the 21st century, and totally extinct in top players' games since alpha go. For the second question, I think a better go player is generally more capable in imagining variations and ideas, so they could surround the centre easier. For Takemiya's natural style, go players usually think Takemiya's white stone, playing natrually was even stronger than his black's opening, trying too hard to play the cosmic style as we have seen. He played the natural style for white, as it is more difficult to build a big moyo with white, so, he would try to maintain balance natrually. He emphasized the natrual style, playing natrually means finding the optimal big point and do not try to get either territories or influence intentionally, which also basically means be flexible. Playing the natural style is logically better than cosmic style (intentionally building big moyo) in opening, so it make sense Takemiya understood playing natrually is better. Yet, understanding the opening especially before AI is so difficult, his cosmic style attempts achieved many national titles and world championships made him a legendary go player loved by many enthusiasts!

@@TakumiGoAcademy oh, interesting, I thought 'natural' and 'cosmic' are kind of similar but your explanation brings more light on the topic - I didn't realize they are actually different terms, thank you for explaining.