Imperial *Authority* has a long tail, all the way back to Capital. The Imperial *Chain of Command* on the other hand, tends to stop at the Sector Duke, and may only get to the Subsector Duke if there is one. If decisions need to be made, including tough, ugly, or messy decisions that affect billions, the Sector Dukes (or the Archdukes as they are re-appointed) are where those decisions land.
Which is, indeed, very much the Age of Sail model.