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.
(1) Yizhang: Very specifically the husband of a maternal aunt.
A/N: Thank you very much for reading! <3 While poor Liu Yao has to wake up at ungodly hours to quarrel with old men, Yan Zheyun gets to remain snuggled up and cosy in bed LOL. There is at least one silver lining to being a concubine over being an emperor...