From the viewpoint of MINAMOTO no Yoritomo, a direct descendant of the Minamoto family, Suesada seems not to have been powerful enough to be Yoritomo's rival because he was related too distantly and was not influential even though he belonged to the same family.
嫡流の源頼朝から見ると、同族ではあるが自分とは血縁的に離れている上に勢力も弱い彼の存在はライバルたり得なかっただろう。