In fact, it would be more appropriate to say that the influence of the samurai of Taira lineage first covered the Togoku where many imperial princes were appointed to the governors of provinces, and later the Taira clan expanded their sphere of influence to the center (the Imperial court) and to the Saigoku.
むしろ親王任国が集中した東国が平氏系武士の盤踞地で、その一族がその後、中央（朝廷）に勢力を伸ばし、西国にも平氏勢力が広がっていったという方が適切である。