Why were European kingdoms ruled by branch families with relations to the main family; instead of rotating dynasties like China or being overthrown by a powerful military leader like Tipu Sultan; and or Saladin; or collapsing like the Gupta and Mughal empires?
This is not a direct answer to the question, but I would stress that conceptualising of political change in China as 'rotating dynasties' is essentially incorrect. See this recent answer for some more context.