Isn't the latter the very definition of Byzantine politics? It's not like its successor system was stable either.
Look at this list of England's kings, starting from the Conquest and ending with the Tudor dynasty:
William I: Arguably usurper
William II: Mysterious death
Henry I: Usurper
Stephen: Usurper
Henry II: War with his own sons
John: War with both his barons and his nephew
Henry III: War with his barons
Edward I
Edward II: Overthrown and possibly murdered
Edward III
Richard II: Overthrown and probably murdered
Henry IV: Usurper, quite a few rebellions and attempted rebellions.
Henry V (although it was a near thing)
Henry VI: Overthrown and murdered
Edward IV: Usurper
Edward V: Overthrown, fate unknown
Richard III: Usurper, overthrown after two years
I'm not saying Byzantine succession was completely peaceful, but its tendency towards violence and coups is exaggerated while at the same time people ignore medieval England (one can compare medieval France as largely stable, but as the infamous Gibbon was an Englishman, I'm looking at his country for comparison) being arguably "wracked with disputed successions and civil war" with at least as much legitimacy as any claim that the ERE was.
There's nothing comparable to the nineteen year long Anarchy either. Even the ten years between Manzikert and Alexius I taking the throne is arguably not as bad for the
people as the
state.