Tonnetz is cute, but it's just another perspective with its own limitations. Why is the double triangle ceg together with egb a nice harmonic chord, but the triangle ceg plus c-eflat-g a disharmony? They form the same shape.
They technically form the same shape, but orientation matters. Triangles pointing up are major, those pointing down are minor. Minor and major chords from the same base note, C
in this case, will have both major and minor tonalities clashing.