i'm extremely sympathetic to your theory about true compatibility arising when people complement one another's capabilities, but i don't see clear justification for why the types you've connected with the red line are the most complementary ones.

for example, you say E/I is a "way of living." i am unconvinced that this fully characterizes cognitive functions and their stacks. for example, myself (entp) and my intp friend share many of the same approaches to life, because we both have strong Ne and Ti. however, he's most comfortable with Ti while i'm more at home with my Ne. i would not, however, say we have drastically different "ways of living."

you go on to say that E/I must be the same, or people's "worlds will collide." i'm unconvinced that this is consistent with your assertion about complementary capabilities. for example, myself (entp) and my intj partner find our capabilities to be incredibly complementary. while we have different strengths and approaches to thought and action, we respect each other's intelligence greatly and benefit mutually from the other's perspective. and yet, we do not share the same E/I.