War of Words
The main benefit to having two prime ministers instead of power consolidated in just a single subject right at the top was one that every emperor, should he wish to retain hold on his political advantage, quickly learnt to reap.
Balance.
The imperial court might be a game of chess for everyone else involved, be it the civil officials or military generals or even the concubines who used their arsenal of charms to help their families gain an edge over their rival factions.
On the surface, it would appear that the emperor was just like any other player of the game, mired deep inside the endless strategies and relentless planning as many moves ahead as he needed to be to keep himself seated on the dragon throne. But one of the first lessons Grand Preceptor Du Yi had taught Liu Yao when he'd first become teacher to the young crown prince, was that a good emperor didn't participate; he made up the rules instead.