Why did the Klingons get rid of the position of Emperor for 300 years? It doesn't seem like the position was abolished through a popular uprising, the Chancellor and the High Council still seem autocratic. The best thing I can assume is after a very incompetent or unstable Emperor came to power 300 years in the past, the Chancellor started a palace coup, had the Emperor killed and abolished the position of Emperor. Since the Emperor in question was extremely unpopular, very few choose to argue against this move.
So instead of being ruled by a hereditary monarch, like an Emperor, the power shifted more directed to the great houses, with the most powerful member of the council being named Chancellor and thus become the head of state.