This is the same way it has worked historically in real life. That's why when someone usurps the thrown (both in real life and in the show with the Targaryens) they slaughter the ex-king's entire family and everyone connected to it. Not just the next in line. Random 2nd cousins and great uncles get cut down too because even their borderline connection to the throne could be a threat if they get the right backer.
So, is this whole story an allegory? If so, which global countries do the houses represent and who is who?I'm going to predict that the real battle is still Littlefinger vs. Varys. Littlefinger gets the South and leaves the north to the Wildings while Varys goes across the narrow sea and rules where Dany is now. Game ends with the houses losing power and power being consolidated into people that had no power before. Thus, democracy is born.