Pretty obvious that they are the ones doing the day to day governament. Imu isn't micromanaging the WG, he was only really show taking direct control on three instances: Uranus, the Nefertari and changing Saturn for Garling, and even on this instances the Gorosei were the one doing the work, he was just ordering.
Through out the story u can se various instances that they are the ones doing the decision making as Head of state of the WG, from joint decisions like choosing the Warlords to taking care of their own "areas' like Saturn with Pacisfista project.
That's literaly what any head of any governament do, u think Putin is fighting in the frontlines, Trump is in the border arresting mexicans and Xi is laying bricks in construction projects? LOL